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Volumn , Issue , 2011, Pages 1-365

Entropy in dynamical systems

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EID: 84926078122     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1017/CBO9780511976155     Document Type: Book
Times cited : (189)

References (145)
  • 1
    • 0038042907 scopus 로고    scopus 로고
    • Exponential approximation for hitting times in mixing processes
    • Paper, electronic
    • Abadi, M. 2001. Exponential approximation for hitting times in mixing processes. Math. Phys. Electron. J., 7, Paper 2, (electronic).
    • (2001) Math. Phys. Electron. J , vol.2
    • Abadi, M.1
  • 2
    • 0013205409 scopus 로고    scopus 로고
    • Inequalities for the occurrence times of rare events in mixing processes. The state of the art
    • Cergy-Pontoise
    • Abadi, M. and Galves, A. 2001. Inequalities for the occurrence times of rare events in mixing processes. The state of the art. Markov Process. Related Fields, 7(1), 97-112. Inhomogeneous random systems (Cergy-Pontoise, 2000).
    • (2001) Inhomogeneous Random Systems , vol.7 , Issue.1 , pp. 97-112
    • Abadi, M.1    Galves, A.2
  • 3
    • 0007410253 scopus 로고
    • The entropy of a derived automorphism
    • Abramov, L. M. 1959. The entropy of a derived automorphism. Dokl. Akad. Nauk SSSR, 128, 647-650.
    • (1959) Dokl. Akad. Nauk SSSR , vol.128 , pp. 647-650
    • Abramov, L.M.1
  • 4
    • 0002623552 scopus 로고
    • Entropy of a skew product of mappings with invariant measure
    • Abramov, L. M. and Rokhlin, V. A. 1962. Entropy of a skew product of mappings with invariant measure. Vestnik Leningrad. Univ., 17(7), 5-13.
    • (1962) Vestnik Leningrad. Univ , vol.17 , Issue.7 , pp. 5-13
    • Abramov, L.M.1    Rokhlin, V.A.2
  • 6
    • 0030304693 scopus 로고    scopus 로고
    • An algebraic approach to the kolmogorov-sinai entropy
    • Alicki, R., Andries, J., Fannes, M. and Tuyls, P. 1996. An algebraic approach to the Kolmogorov-Sinai entropy. Rev. Math. Phys., 8(2), 167-184.
    • (1996) Rev. Math. Phys , vol.8 , Issue.2 , pp. 167-184
    • Alicki, R.1    Ries, J.2    Fannes, M.3    Tuyls, P.4
  • 7
    • 0004126711 scopus 로고
    • London Mathematical Society Monographs, London: Academic Press Inc. [Harcourt Brace Jovanovich Publishers]
    • Asimow, L. and Ellis, A. J. 1980. Convexity Theory and Its Applications in Functional Analysis. London Mathematical Society Monographs, vol. 16. London: Academic Press Inc. [Harcourt Brace Jovanovich Publishers].
    • (1980) Convexity Theory and Its Applications in Functional Analysis , vol.16
    • Asimow, L.1    Ellis, A.J.2
  • 8
    • 0001336132 scopus 로고
    • Three observations on linear algebra
    • Birkhoff, G. 1946. Three observations on linear algebra. Univ. Nac. Tucumaen. Revista A., 5, 147-151.
    • (1946) Univ. Nac. Tucumaen. Revista A , vol.5 , pp. 147-151
    • Birkhoff, G.1
  • 9
    • 0002754147 scopus 로고
    • A disjointness theorem involving topological entropy
    • Blanchard, F. 1993. A disjointness theorem involving topological entropy. Bull. Soc. Math. France, 121(4), 465-478.
    • (1993) Bull. Soc. Math. France , vol.121 , Issue.4 , pp. 465-478
    • Blanchard, F.1
  • 11
    • 0010765078 scopus 로고
    • Zero entropy factors of topological flows
    • Blanchard, F. and Lacroix, Y. 1993. Zero entropy factors of topological flows. Proc. Amer. Math. Soc., 119(3), 985-992.
    • (1993) Proc. Amer. Math. Soc , vol.119 , Issue.3 , pp. 985-992
    • Blanchard, F.1    Lacroix, Y.2
  • 12
    • 0000075267 scopus 로고
    • U ber die beziehung dem zweiten haubtsatze der mechanischen warmetheorie und der wahrscheinlichkeitsrechnung respektive den satzen uber das warmegleichgewicht
    • Boltzmann, L. 1877. U ber die beziehung dem zweiten Haubtsatze der mechanischen Warmetheorie und der Wahrscheinlichkeitsrechnung respektive den Satzen uber das Warmegleichgewicht. Wiener Berichte, 76, 373-435.
    • (1877) Wiener Berichte , vol.76 , pp. 373-435
    • Boltzmann, L.1
  • 13
    • 84942990301 scopus 로고
    • Entropyfor group endomorphisms and homogeneous spaces
    • Bowen, R. 1971. Entropy for group endomorphisms and homogeneous spaces. Trans. Amer. Math. Soc., 153, 401-414.
    • (1971) Trans. Amer. Math. Soc , vol.153 , pp. 401-414
    • Bowen, R.1
  • 14
    • 0344430376 scopus 로고
    • Lowerentropyfactorsof sofic systems
    • Boyle, M. 1983. Lower entropy factors of sofic systems. Ergodic Theory Dynam. Systems, 3(4), 541-557.
    • (1983) Ergodic Theory Dynam. Systems , vol.3 , Issue.4 , pp. 541-557
    • Boyle, M.1
  • 16
    • 1842486728 scopus 로고    scopus 로고
    • The entropy theory of symbolic extensions
    • Boyle, M. and Downarowicz, T. 2004. The entropy theory of symbolic extensions. Invent. Math., 156(1), 119-161.
    • (2004) Invent. Math , vol.156 , Issue.1 , pp. 119-161
    • Boyle, M.1    Downarowicz, T.2
  • 17
    • 33748580382 scopus 로고    scopus 로고
    • Symbolic extension entropy: Cr examples, products and flows
    • Boyle, M. and Downarowicz, T. 2006. Symbolic extension entropy: Cr examples, products and flows. Discrete Contin. Dyn. Syst., 16(2), 329-341.
    • (2006) Discrete Contin. Dyn. Syst , vol.16 , Issue.2 , pp. 329-341
    • Boyle, M.1    Downarowicz, T.2
  • 18
    • 0036048137 scopus 로고    scopus 로고
    • Residual entropy, conditional entropy and subshift covers
    • Boyle, M., Fiebig, D. and Fiebig, U.-R. 2002. Residual entropy, conditional entropy and subshift covers. Forum Math., 14(5), 713-757.
    • (2002) Forum Math , vol.14 , Issue.5 , pp. 713-757
    • Boyle, M.1    Fiebig, D.2    Fiebig, U.-R.3
  • 19
    • 0001531440 scopus 로고
    • The individual ergodic theorem of information theory
    • Breiman, L. 1957. The individual ergodic theorem of information theory. Ann. Math. Statist., 28, 809-811.
    • (1957) Ann. Math. Statist , vol.28 , pp. 809-811
    • Breiman, L.1
  • 20
    • 0002467622 scopus 로고
    • On local entropy, in geometic dynamics (Rio de janeiro 1981)
    • Berlin: Springer-Verlag
    • Brin, M. and Katok, A. 1983. On local entropy, in Geometic Dynamics (Rio de Janeiro 1981). Springer Lecture Notes in Mathematics, vol. 1007. Berlin: Springer-Verlag, pp. 30-38.
    • (1983) Springer Lecture Notes in Mathematics , vol.1007 , pp. 30-38
    • Brin, M.1    Katok, A.2
  • 21
    • 34250499738 scopus 로고
    • Asymptotic properties of expansive homeomorphisms
    • Bryant, B. F., and Walters, P. 1969. Asymptotic properties of expansive homeomorphisms. Math. Systems Theory, 3, 60-66.
    • (1969) Math. Systems Theory , vol.3 , pp. 60-66
    • Bryant, B.F.1    Walters, P.2
  • 22
    • 84926117034 scopus 로고    scopus 로고
    • C2 surface diffeomorphisms have symbolic extensions
    • Print
    • Burguet, D. C2 surface diffeomorphisms have symbolic extensions. Invent. Math. in print.
    • Invent. Math
    • Burguet, D.1
  • 23
    • 80052812928 scopus 로고    scopus 로고
    • Symbolic extensions for nonuniformly entropy expanding maps
    • Burguet, D. 2010. Symbolic extensions for nonuniformly entropy expanding maps. Colloq. Math., 121, 129-151.
    • (2010) Colloq. Math , vol.121 , pp. 129-151
    • Burguet, D.1
  • 24
    • 80052935266 scopus 로고    scopus 로고
    • Entropie et complexitee locale des systemes dynamiques diffeerentiables
    • Unpublished
    • Burguet, D. 2008. Entropie et complexitee locale des systemes dynamiques diffeerentiables. Doctoral Dissertation. Unpublished.
    • (2008) Doctoral dissertation
    • Burguet, D.1
  • 25
    • 69849086665 scopus 로고    scopus 로고
    • A direct proof of the tail variational principle and its extension to maps
    • Burguet, D. 2009. A direct proof of the tail variational principle and its extension to maps. Ergodic Theory Dynam. Systems, 29(2), 357-369.
    • (2009) Ergodic Theory Dynam. Systems , vol.29 , Issue.2 , pp. 357-369
    • Burguet, D.1
  • 26
    • 77950228660 scopus 로고    scopus 로고
    • Examples of
    • Burguet, D. 2010. Examples of Crinterval map with large symbolic extension entropy. Discrete Contin. Dyn. Syst., 26(3), 873-899.
    • (2010) Discrete Contin. Dyn. Syst , vol.26 , Issue.3 , pp. 873-899
    • Burguet, D.1
  • 27
    • 84926082643 scopus 로고    scopus 로고
    • Orders of accumulation of entropy
    • Print
    • Burguet, D. and McGoff, K. Orders of accumulation of entropy. Fund. Math. in print.
    • Fund. Math
    • Burguet, D.1    Mc Goff, K.2
  • 28
    • 52649161571 scopus 로고    scopus 로고
    • Residuality of dynamical morphisms
    • 84/85(, part 2), Dedicated to the memory of Anzelm Iwanik
    • Burton, R. M., Keane, M. S. and Serafin, J. 2000. Residuality of dynamical morphisms. Colloq. Math., 84/85(, part 2), 307-317. Dedicated to the memory of Anzelm Iwanik.
    • (2000) Colloq. Math , pp. 307-317
    • Burton, R.M.1    Keane, M.S.2    Serafin, J.3
  • 29
    • 0003284881 scopus 로고    scopus 로고
    • Intrinsic ergodicity of smooth interval maps
    • Buzzi, J. 1997. Intrinsic ergodicity of smooth interval maps. Israel J. Math., 100, 125-161.
    • (1997) Israel J. Math , vol.100 , pp. 125-161
    • Buzzi, J.1
  • 30
    • 0003739797 scopus 로고
    • Paris: Bachelier. French title: Reflexions sur la puissance motrice du feu et sur les machines propres a deevelopper cette puissance
    • Carnot, S. 1824. Reflections on the Motive Power of Fire and on Machines Fitted to Develop that Power. Paris: Bachelier. French title: Reflexions sur la puissance motrice du feu et sur les machines propres a deevelopper cette puissance.
    • (1824) Reflections on the Motive Power of Fire and on Machines Fitted to Develop that Power
    • Carnot, S.1
  • 32
    • 84926117325 scopus 로고
    • Edited by J. Marsden, T. Lance and S. Gelbart. New York, Amsterdam: W. A. Benjamin, Inc
    • Choquet, G. 1969. Lectures on Analysis. Vol. II: Representation Theory. Edited by J. Marsden, T. Lance and S. Gelbart. New York, Amsterdam: W. A. Benjamin, Inc.
    • (1969) Lectures on Analysis. Vol. II: Representation Theory , vol.2
    • Choquet, G.1
  • 33
    • 0000931548 scopus 로고
    • A note on the ergodic theorem of information theory
    • Chung, K. L. 1961. A note on the ergodic theorem of information theory. Ann. Math. Statist., 32, 612-614.
    • (1961) Ann. Math. Statist , vol.32 , pp. 612-614
    • Chung, K.L.1
  • 34
  • 35
    • 84926106873 scopus 로고
    • U ber die bewegende Kraft der Warme, Part I, Part II
    • 9, 368-397, 500-524. English translation “On the Moving Force of Heat, and the Laws regarding the Nature of Heat itself which are deducible therefrom” Phil. Mag. (1851)
    • Clausius, R. 1850. U ber die bewegende Kraft der Warme, Part I, Part II. Annalen der Physik, 79, 368-397, 500-524. English translation “On the Moving Force of Heat, and the Laws regarding the Nature of Heat itself which are deducible therefrom” Phil. Mag. (1851), 2, 1-21, 102-119.
    • (1850) Annalen der Physik , vol.2 , Issue.1-21 , pp. 102-119
    • Clausius, R.1
  • 36
    • 0011418599 scopus 로고    scopus 로고
    • Asymptotic Laws for Symbolic Dynamical Systems
    • London Mathematical Society Lecture Note Series, Cambridge: Cambridge University Press
    • Coelho, Z. 2000. Asymptotic laws for symbolic dynamical systems, in Topics in Symbolic Dynamics and Applications(Temuco, 1997). London Mathematical Society Lecture Note Series, vol. 279. Cambridge: Cambridge University Press, pp. 123-165.
    • (1997) Topics in Symbolic Dynamics and Applications , vol.279 , pp. 123-165
    • Coelho, Z.1
  • 37
    • 84889281816 scopus 로고
    • New York:John Wiley & Sons Inc. A Wiley-Interscience Publication
    • Cover, T. M. and Thomas, J. A. 1991. Elements of Information Theory. Wiley Series in Telecommunications. New York: John Wiley & Sons Inc. A Wiley-Interscience Publication.
    • (1991) Elements of Information Theory
    • Cover, T.M.1    Thomas, J.A.2
  • 38
    • 77954568632 scopus 로고
    • Finitary codes between one-sided bernoulli shifts
    • del Junco, A. 1981. Finitary codes between one-sided Bernoulli shifts. Ergodic Theory Dynam. Systems, 1(3), 285-301 (1982).
    • (1982) Ergodic Theory Dynam. Systems , vol.1 , Issue.3 , pp. 285-301
    • Del Junco, A.1
  • 39
    • 34250012263 scopus 로고    scopus 로고
    • Dynamical bias in the coin toss
    • Diaconis, P., Holmes, S. and Montgomery, R. 2007. Dynamical bias in the coin toss. SIAM Rev., 49(2), 211-235.
    • (2007) SIAM Rev , vol.49 , Issue.2 , pp. 211-235
    • Diaconis, P.1    Holmes, S.2    Montgomery, R.3
  • 40
    • 0039301860 scopus 로고
    • A correlation between topological entropy and metric entropy
    • Dinaburg, E. I. 1970. A correlation between topological entropy and metric entropy. Dokl. Akad. Nauk SSSR, 190, 19-22.
    • (1970) Dokl. Akad. Nauk SSSR , vol.190 , pp. 19-22
    • Dinaburg, E.I.1
  • 41
    • 0035600854 scopus 로고    scopus 로고
    • Entropyof a symbolic extension of a dynamical system
    • Downarowicz, T. 2001. Entropy of a symbolic extension of a dynamical system. Ergodic Theory Dynam. Systems, 21(4), 1051-1070.
    • (2001) Ergodic Theory Dynam. Systems , vol.21 , Issue.4 , pp. 1051-1070
    • Downarowicz, T.1
  • 42
    • 27944496411 scopus 로고    scopus 로고
    • Entropy structure
    • Downarowicz, T. 2005a. Entropy structure. J.Anal. Math., 96, 57-116.
    • (2005) J.Anal. Math , vol.96 , pp. 57-116
    • Downarowicz, T.1
  • 43
    • 33645775368 scopus 로고    scopus 로고
    • Surveyof odometers and toeplitz flows
    • Providence, RI: American Mathematical Society
    • Downarowicz, T. 2005b. Survey of odometers and Toeplitz flows, in Algebraic and Topological Dynamics. Contemporary Mathematics, vol. 385. Providence, RI: American Mathematical Society, pp. 7-37.
    • (2005) Algebraic and Topological Dynamics , vol.385 , pp. 7-37
    • Downarowicz, T.1
  • 44
    • 33847743788 scopus 로고    scopus 로고
    • Minimal models for noninvertible and not uniquely ergodic systems
    • Downarowicz, T. 2006. Minimal models for noninvertible and not uniquely ergodic systems. Israel J. Math., 156, 93-110.
    • (2006) Israel J. Math , vol.156 , pp. 93-110
    • Downarowicz, T.1
  • 45
    • 58449089479 scopus 로고    scopus 로고
    • Facesof simplexes of invariant measures
    • Downarowicz, T. 2008. Faces of simplexes of invariant measures. Israel J. Math., 165, 189-210.
    • (2008) Israel J. Math , vol.165 , pp. 189-210
    • Downarowicz, T.1
  • 46
    • 17044379859 scopus 로고    scopus 로고
    • Measure-theoretic and topological entropy of operators on function spaces
    • Downarowicz, T. and Frej, B. 2005. Measure-theoretic and topological entropy of operators on function spaces. Ergodic Theory Dynam. Systems, 25(2), 455-481.
    • (2005) Ergodic Theory Dynam. Systems , vol.25 , Issue.2 , pp. 455-481
    • Downarowicz, T.1    Frej, B.2
  • 47
    • 78149308089 scopus 로고    scopus 로고
    • Attracting and repelling in homogeneous signal processes
    • Downarowicz, T., Grzegorek, P. and Lacroix, Y. 2010. Attracting and repelling in homogeneous signal processes. Nonlinearity, 23(11), 2793-2813.
    • (2010) Nonlinearity , vol.23 , Issue.11 , pp. 2793-2813
    • Downarowicz, T.1    Grzegorek, P.2    Lacroix, Y.3
  • 50
    • 84871110496 scopus 로고    scopus 로고
    • Topological entropy zero and asymptotic pairs
    • Print
    • Downarowicz, T. and Lacroix, Y. Topological entropy zero and asymptotic pairs. Israel J. Math. in print.
    • Israel J. Math
    • Downarowicz, T.1    Lacroix, Y.2
  • 51
    • 78049489967 scopus 로고    scopus 로고
    • Spontaneous clustering in theoretical and some empirical stochastic processes
    • Downarowicz, T., Lacroix, Y. and Leandri, D. 2010. Spontaneous clustering in theoretical and some empirical stochastic processes. ESAIM. Probab. Statist., 14, 256-262.
    • (2010) ESAIM. Probab. Statist , vol.14 , pp. 256-262
    • Downarowicz, T.1    Lacroix, Y.2    Leandri, D.3
  • 52
    • 67349202120 scopus 로고    scopus 로고
    • Smooth interval maps have symbolic extensions: The antarctic theorem
    • Downarowicz, T. and Maass, A. 2009. Smooth interval maps have symbolic extensions: the antarctic theorem. Invent. Math., 176(3), 617-636.
    • (2009) Invent. Math , vol.176 , Issue.3 , pp. 617-636
    • Downarowicz, T.1    Maass, A.2
  • 53
    • 18244372671 scopus 로고    scopus 로고
    • Symbolic extensions and smooth dynamical systems
    • Downarowicz, T. and Newhouse, S. E. 2005. Symbolic extensions and smooth dynamical systems. Invent. Math., 160(3), 453-499.
    • (2005) Invent. Math , vol.160 , Issue.3 , pp. 453-499
    • Downarowicz, T.1    Newhouse, S.E.2
  • 54
    • 0036994010 scopus 로고    scopus 로고
    • Fiber entropy and conditional variational principle in compact non-metrizable spaces
    • Downarowicz, T. and Serafin, J. 2002. Fiber entropy and conditional variational principle in compact non-metrizable spaces. Fund. Math., 172(3), 217-247.
    • (2002) Fund. Math , vol.172 , Issue.3 , pp. 217-247
    • Downarowicz, T.1    Serafin, J.2
  • 55
    • 0041410203 scopus 로고    scopus 로고
    • Possible entropy functions
    • Downarowicz, T. and Serafin, J. 2003. Possible entropy functions. Israel J. Math., 135, 221-250.
    • (2003) Israel J. Math , vol.135 , pp. 221-250
    • Downarowicz, T.1    Serafin, J.2
  • 57
    • 0035402927 scopus 로고    scopus 로고
    • Limit laws of entrance times for low-complexity cantor minimal systems
    • Durand, F. and Maass, A. 2001. Limit laws of entrance times for low-complexity Cantor minimal systems. Nonlinearity, 14(4), 683-700.
    • (2001) Nonlinearity , vol.14 , Issue.4 , pp. 683-700
    • Durand, F.1    Maass, A.2
  • 60
    • 33645159044 scopus 로고    scopus 로고
    • Malickye-riecan’s entropy as a version of operator entropy
    • Frej, B. 2006. Malickye-Riecan’s entropy as a version of operator entropy. Fund. Math., 189(2), 185-193.
    • (2006) Fund. Math , vol.189 , Issue.2 , pp. 185-193
    • Frej, B.1
  • 62
    • 33646727744 scopus 로고
    • Disjointness in ergodic theory, minimal sets, and a problem in diophantine approximation
    • Furstenberg, H. 1967. Disjointness in ergodic theory, minimal sets, and a problem in Diophantine approximation. Math. Systems Theory, 1, 1-49.
    • (1967) Math. Systems Theory , vol.1 , pp. 1-49
    • Furstenberg, H.1
  • 65
    • 84968668270 scopus 로고    scopus 로고
    • Providence, RI: American Mathematical Society
    • Glasner, S. 2003. Ergodic Theory via Joinings. Mathematical Surveys and Monographs, vol. 101. Providence, RI: American Mathematical Society.
    • (2003) Ergodictheory via Joinings , pp. 101
    • Glasner, S.1
  • 66
    • 0038587571 scopus 로고    scopus 로고
    • Quasifactors of ergodic systems with positive entropy
    • Glasner, S. and Weiss, B. 2003. Quasifactors of ergodic systems with positive entropy. Israel J. Math., 134, 363-380.
    • (2003) Israel J. Math , vol.134 , pp. 363-380
    • Glasner, S.1    Weiss, B.2
  • 67
    • 0001400518 scopus 로고
    • Relating topological entropy and measure entropy
    • Goodman, T. N. T. 1971. Relating topological entropy and measure entropy. Bull. London Math. Soc., 3, 176-180.
    • (1971) Bull. London Math. Soc , vol.3 , pp. 176-180
    • Goodman, T.N.T.1
  • 68
    • 84926090592 scopus 로고
    • Topologicalentropybounds measure-theoretic entropy
    • Lecture Notes in Mathematics, Berlin: Springer-Verlag
    • Goodwyn, L. W. 1971. Topological entropy bounds measure-theoretic entropy, in Global Differentiable Dynamics. Lecture Notes in Mathematics, vol. 235 Berlin: Springer-Verlag, pp. 69-84.
    • (1971) Global Differentiable Dynamics , vol.235 , pp. 69-84
    • Goodwyn, L.W.1
  • 69
    • 65249147179 scopus 로고    scopus 로고
    • Return times in a process generated by a typical partition
    • Grzegorek, P. and Kupsa, M. 2009. Return times in a process generated by a typical partition. Nonlinearity, 22(2), 371-379.
    • (2009) Nonlinearity , vol.22 , Issue.2 , pp. 371-379
    • Grzegorek, P.1    Kupsa, M.2
  • 71
    • 27644545715 scopus 로고    scopus 로고
    • Hitting and return times in ergodic dynamical systems
    • Haydn, N., Lacroix, Y. and Vaienti, S. 2005. Hitting and return times in ergodic dynamical systems. Ann. Probab., 33(5), 2043-2050.
    • (2005) Ann. Probab , vol.33 , Issue.5 , pp. 2043-2050
    • Haydn, N.1    Lacroix, Y.2    Vaienti, S.3
  • 72
    • 0033426519 scopus 로고    scopus 로고
    • Statistics of return times: A general framework and new applications
    • Hirata, M., Saussol, B. and Vaienti, S. 1999. Statistics of return times: a general framework and new applications. Comm. Math. Phys., 206(1), 33-55.
    • (1999) Comm. Math. Phys , vol.206 , Issue.1 , pp. 33-55
    • Hirata, M.1    Saussol, B.2    Vaienti, S.3
  • 73
    • 0004188206 scopus 로고
    • Graduate Texts in Mathematics, New York: Springer-Verlag. Corrected reprint of the 1976 original
    • Hirsch, M. W. 1994. Differential Topology. Graduate Texts in Mathematics, vol. 33. New York: Springer-Verlag. Corrected reprint of the 1976 original.
    • (1994) Differential Topology , vol.33
    • Hirsch, M.W.1
  • 74
    • 84974513208 scopus 로고
    • On topological entropy of maps
    • Hurley, M. 1995. On topological entropy of maps. Ergodic Theory Dynam. Systems, 15(3), 557-568.
    • (1995) Ergodic Theory Dynam. Systems , vol.15 , Issue.3 , pp. 557-568
    • Hurley, M.1
  • 78
    • 68149089788 scopus 로고
    • On the notion of recurrence in discrete stochastic processes
    • Kac, M. 1947. On the notion of recurrence in discrete stochastic processes. Bull. Amer. Math. Soc., 53, 1002-1010.
    • (1947) Bull. Amer. Math. Soc , vol.53 , pp. 1002-1010
    • Kac, M.1
  • 79
    • 0001293509 scopus 로고
    • T, T−1 transformation is not loosely Bernoulli
    • Kalikow, S. A. 1982. T, T−1 transformation is not loosely Bernoulli. Ann. of Math. (2), 115(2), 393-409.
    • (1982) Ann. Of Math , vol.115 , Issue.2 , pp. 393-409
    • Kalikow, S.A.1
  • 80
    • 4043057615 scopus 로고    scopus 로고
    • A note on the entropy of a doubly stochastic operator
    • Kamineski, B. and, 84/85, (, part 1), Dedicated to the memory of Anzelm Iwanik
    • Kamineski, B. and de Sam Lazaro, J. 2000. A note on the entropy of a doubly stochastic operator. Colloq. Math., 84/85(, part 1), 245-254. Dedicated to the memory of Anzelm Iwanik.
    • (2000) Colloq. Math , pp. 245-254
    • De Sam Lazaro, J.1
  • 81
    • 69849088295 scopus 로고    scopus 로고
    • The determinism and the kolmogorov property in topological dynamics
    • Kamineski, B., and Szymaneski, J
    • Kamineski, B., Siemaszko, A. and Szymaneski, J. 2003. The determinism and the Kolmogorov property in topological dynamics. Bull. Polish Acad. Sci. Math., 51(4), 401-417.
    • (2003) Bull. Polish Acad. Sci. Math , vol.51 , Issue.4 , pp. 401-417
    • Siemaszko, A.1
  • 83
    • 51649161951 scopus 로고
    • Lyapunov exponents, entropyand periodic orbits for diffeomorphisms
    • Katok, A. 1980. Lyapunov exponents, entropy and periodic orbits for diffeomorphisms. Inst. Hautes Eetudes Sci. Publ. Math., 137-173.
    • (1980) Inst. Hautes Eetudes Sci. Publ. Math , pp. 137-173
    • Katok, A.1
  • 84
    • 70350644614 scopus 로고    scopus 로고
    • Fifty years of entropy in dynamics: 1958-2007
    • Katok, A. 2007. Fifty years of entropy in dynamics: 1958-2007. J. Mod. Dyn., 1(4), 545-596.
    • (2007) J. Mod. Dyn , vol.1 , Issue.4 , pp. 545-596
    • Katok, A.1
  • 85
    • 0003406478 scopus 로고
    • Cambridge: Cambridge University Press. With a supplementary chapter by Katok and Leonardo Mendoza
    • Katok, A. and Hasselblatt, B. 1995. Introductionto the Modern Theory of Dynamical Systems. Encyclopedia of Mathematics and its Applications, vol. 54. Cambridge: Cambridge University Press. With a supplementary chapter by Katok and Leonardo Mendoza.
    • (1995) Introduction , pp. 54
    • Katok, A.1    Hasselblatt, B.2
  • 86
    • 0000182509 scopus 로고
    • Bernoulli schemes of the same entropy are finitarily isomorphic
    • Keane, M. S. and Smorodinsky, M. 1979. Bernoulli schemes of the same entropy are finitarily isomorphic. Ann. of Math. (2), 109(2), 397-406.
    • (1979) Ann. Of Math , vol.109 , Issue.2-2 , pp. 397-406
    • Keane, M.S.1    Smorodinsky, M.2
  • 87
    • 0001450585 scopus 로고
    • A new metric invariant of transient dynamical systems and automorphisms in lebesgue spaces
    • Kolmogorov, A. N. 1958. A new metric invariant of transient dynamical systems and automorphisms in Lebesgue spaces. Dokl. Akad. Nauk SSSR (N.S.), 119, 861-864.
    • (1958) Dokl. Akad. Nauk SSSR (N.S.) , vol.119 , pp. 861-864
    • Kolmogorov, A.N.1
  • 88
    • 0001494176 scopus 로고
    • Entropyper unit time as a metric invariant of automorphisms
    • Kolmogorov, A. N. 1959. Entropy per unit time as a metric invariant of automorphisms. Dokl. Akad. Nauk SSSR, 124, 754-755.
    • (1959) Dokl. Akad. Nauk SSSR , vol.124 , pp. 754-755
    • Kolmogorov, A.N.1
  • 89
    • 0003665284 scopus 로고
    • Berlin: Walter de Gruyter & Co. With a supplement by Antoine Brunel
    • Krengel, U. 1985. Ergodic Theorems. de Gruyter Studies in Mathematics, vol. 6. Berlin: Walter de Gruyter & Co. With a supplement by Antoine Brunel.
    • (1985) Ergodictheorems , pp. 6
    • Krengel, U.1
  • 90
    • 84966257945 scopus 로고
    • On entropy and generators of measure-preserving transformations
    • Krieger, W. 1970. On entropy and generators of measure-preserving transformations. Trans.Amer. Math. Soc., 149, 453-464.
    • (1970) Trans , vol.149 , pp. 453-464
    • Krieger, W.1
  • 91
    • 80054968274 scopus 로고
    • Miracles and statistics: The casual assumption of independence
    • Kruskal, W. 1988. Miracles and statistics: The casual assumption of independence. J. Amer.Statist. Assoc., 83(404), 929-940.
    • (1988) J. Amer.Statist. Assoc , vol.83 , Issue.404 , pp. 929-940
    • Kruskal, W.1
  • 92
    • 0002651817 scopus 로고
    • La theeorie geeneerale de la mesure dans son application al’eetude des systemes dynamiques de la meecanique non lineeaire
    • Kryloff, N. and Bogoliouboff, N. 1937. La theeorie geeneerale de la mesure dans son application al’eetude des systemes dynamiques de la meecanique non lineeaire. Ann. of Math. (2), 38(1), 65-113.
    • (1937) Ann. Of Math , vol.38 , Issue.1-2 , pp. 65-113
    • Kryloff, N.1    Bogoliouboff, N.2
  • 93
    • 0040913682 scopus 로고
    • Entropy, transverse entropy and partitions of unity
    • Langevin, R. and Walczak, P. 1994. Entropy, transverse entropy and partitions of unity. ErgodicTheory Dynam. Systems, 14(3), 551-563.
    • (1994) Ergodic , vol.14 , Issue.3 , pp. 551-563
    • Langevin, R.1    Walczak, P.2
  • 94
    • 0041688943 scopus 로고
    • A variational principle for the topological conditional entropy, in ergodic theory
    • Lect. Notes Math. Springer
    • Ledrappier, F. 1979. A variational principle for the topological conditional entropy, in Ergodic theory, Proc., Oberwolfach 1978. Lect. Notes Math. 729, Springer. pp. 78-88.
    • (1979) Proc., Oberwolfach 1978 , vol.729 , pp. 78-88
    • Ledrappier, F.1
  • 95
    • 84959811336 scopus 로고
    • A relativised variational principle for continuous transformations
    • Ledrappier, F. and Walters, P. 1977. A relativised variational principle for continuous transformations. J. London Math. Soc. (2), 16(3), 568-576.
    • (1977) J.London Math. Soc , vol.16 , Issue.3-2 , pp. 568-576
    • Ledrappier, F.1    Walters, P.2
  • 96
    • 0013196827 scopus 로고    scopus 로고
    • 1999. Mean dimension, small entropy factors and an embedding theorem
    • Lindenstrauss, E. 1999. Mean dimension, small entropy factors and an embedding theorem. Inst. Hautes etudes Sci. Publ. Math., 227-262 (2000).
    • (1999) Inst. Hautes etudes Sci. Publ. Math , Issue.2000 , pp. 227-262
    • Lindenstrauss, E.1
  • 97
  • 98
    • 0032105273 scopus 로고    scopus 로고
    • Pesin’sentropyformula for endomorphisms
    • Liu, P.-D. 1998. Pesin’s entropy formula for endomorphisms. Nagoya Math. J., 150, 197-209.
    • (1998) Nagoya Math. J , vol.150 , pp. 197-209
    • Liu, P.-D.1
  • 99
    • 0033722485 scopus 로고    scopus 로고
    • Dynamical entropy for markov operators
    • Makarov, I. I. 2000. Dynamical entropy for Markov operators. J Dynam. Control Systems, 6(1), 1-11.
    • (2000) J Dynam. Control Systems , vol.6 , Issue.1 , pp. 1-11
    • Makarov, I.I.1
  • 102
    • 0004142546 scopus 로고
    • Unveranderter Nachdruck der ersten Auflage von 1932. Die Grundlehren der mathematischen Wissenschaften, Band. Dover Publications, Inc
    • Maxwell, J. C. 1871. Theory of Heat. Unveranderter Nachdruck der ersten Auflage von 1932. Die Grundlehren der mathematischen Wissenschaften, Band 38. Dover Publications, Inc.
    • (1871) Theory of Heat , pp. 38
    • Maxwell, J.C.1
  • 103
    • 84926087192 scopus 로고
    • Orders of accumulation of entropy on manifolds
    • Print
    • McGoff, K. Orders of accumulation of entropy on manifolds. J. Anal. Math. in print.
    • (1953) J.Anal. Math
    • Mc Goff, K.1
  • 104
    • 0001413858 scopus 로고
    • The basic theorems of information theory
    • McMillan, B. 1953. The basic theorems of information theory. Ann. Math. Statistics, 24, 196-219.
    • (1953) Ann. Math. Statistics , vol.24 , pp. 196-219
    • Mc Millan, B.1
  • 105
    • 0009302187 scopus 로고
    • A case of isomorphism of bernoulli schemes
    • Mesalkin, L. D. 1959. A case of isomorphism of Bernoulli schemes. Dokl. Akad. Nauk SSSR, 128, 41-44.
    • (1959) Dokl. Akad. Nauk SSSR , vol.128 , pp. 41-44
    • Mesalkin, L.D.1
  • 106
    • 0000158223 scopus 로고
    • Topological conditional entropy
    • Misiurewicz, M. 1976. Topological conditional entropy. Studia Math., 55(2), 175-200.
    • (1976) Studia Math , vol.55 , Issue.2 , pp. 175-200
    • Misiurewicz, M.1
  • 110
    • 0001685281 scopus 로고
    • Continuity properties of entropy
    • Newhouse, S. E. 1989. Continuity properties of entropy. Ann. of Math., 129(2), 215-235.
    • (1989) Ann. Of Math , vol.129 , Issue.2 , pp. 215-235
    • Newhouse, S.E.1
  • 111
    • 0000262299 scopus 로고
    • Corrections to: “Continuity properties of entropy
    • [Ann. of Math. (2) 129 (1989), no. 2, 215-235]
    • Newhouse, S. E. 1990. Corrections to: “Continuity properties of entropy” [Ann. of Math. (2) 129 (1989), no. 2, 215-235]. Ann. of Math., 131(2), 409-410.
    • (1990) Ann. Of Math , vol.131 , Issue.2 , pp. 409-410
    • Newhouse, S.E.1
  • 112
  • 113
    • 0000768820 scopus 로고
    • Bernoulli shifts with the same entropy are isomorphic
    • 1970
    • Ornstein, D. S. 1970a. Bernoulli shifts with the same entropy are isomorphic. Advances in Math., 4, 337-352 (1970).
    • (1970) Advances in Math , vol.4 , pp. 337-352
    • Ornstein, D.S.1
  • 114
    • 0011400243 scopus 로고
    • Factors of bernoulli shifts are bernoulli shifts
    • 1970
    • Ornstein, D. S. 1970b. Factors of Bernoulli shifts are Bernoulli shifts. Advances in Math., 5, 349-364 (1970).
    • (1970) Advances in Math , vol.5 , pp. 349-364
    • Ornstein, D.S.1
  • 115
    • 0000768821 scopus 로고
    • Two bernoulli shifts with infinite entropy are isomorphic
    • 1970
    • Ornstein, D. S. 1970c. Two Bernoulli shifts with infinite entropy are isomorphic. Advances in Math., 5, 339-348 (1970).
    • (1970) Advances in Math , vol.5 , pp. 339-348
    • Ornstein, D.S.1
  • 116
    • 0041112033 scopus 로고
    • An example of a kolmogorov automorphism that is not a bernoulli shift
    • Ornstein, D. S. 1973. An example of a Kolmogorov automorphism that is not a Bernoulli shift. Advances in Math., 10, 49-62.
    • (1973) Advances in Math , vol.10 , pp. 49-62
    • Ornstein, D.S.1
  • 117
    • 43449108492 scopus 로고
    • An uncountable family of
    • Ornstein, D. S. and Shields, P. C. 1973. An uncountable family of K-automorphisms. Advances in Math., 10, 63-88.
    • (1973) Advances in Math , vol.10 , pp. 63-88
    • Ornstein, D.S.1    Shields, P.C.2
  • 118
    • 51249190681 scopus 로고
    • Everytransformation is bilaterally deterministic
    • Conference on Ergodic Theory and Topological Dynamics (Kibbutz Lavi, 1974)
    • Ornstein, D. S. and Weiss, B. 1975. Every transformation is bilaterally deterministic. Israel J. Math., 21(2-3), 154-158. Conference on Ergodic Theory and Topological Dynamics (Kibbutz Lavi, 1974).
    • (1975) Israel J. Math , vol.21 , Issue.2-3 , pp. 154-158
    • Ornstein, D.S.1    Weiss, B.2
  • 119
    • 0027266419 scopus 로고
    • Entropyand data compression schemes
    • Ornstein, D. S. and Weiss, B. 1993. Entropy and data compression schemes. IEEE Trans. Inform. Theory, 39(1), 78-83.
    • (1993) IEEE Trans. Inform. Theory , vol.39 , Issue.1 , pp. 78-83
    • Ornstein, D.S.1    Weiss, B.2
  • 120
    • 0038434713 scopus 로고
    • A multiplicative ergodic theorem. Characteristic ljapunov, exponents of dynamical systems
    • Oseledets, V. I. 1968. A multiplicative ergodic theorem. Characteristic Ljapunov, exponents of dynamical systems. Trudy Moskov. Mat. Obsc., 19, 179-210.
    • (1968) Trudy Moskov. Mat. Obsc , vol.19 , pp. 179-210
    • Oseledets, V.I.1
  • 122
    • 84961291543 scopus 로고
    • Characteristic ljapunov exponents, and smooth ergodic theory
    • 287
    • Pesin, Y. B. 1977. Characteristic Ljapunov exponents, and smooth ergodic theory. Uspehi Mat. Nauk, 32(4 (196)), 55-112, 287.
    • (1977) Uspehi Mat. Nauk , vol.32 , Issue.4-196 , pp. 55-112
    • Pesin, Y.B.1
  • 123
    • 0003831421 scopus 로고
    • Cambridge Studies in Advanced Mathematics, Cambridge: Cambridge University Press
    • Petersen, K. 1983. Ergodic Theory. Cambridge Studies in Advanced Mathematics, vol. 2. Cambridge: Cambridge University Press.
    • (1983) Ergodic theory , vol.2
    • Petersen, K.1
  • 124
    • 0038452486 scopus 로고    scopus 로고
    • Second edn. Lecture Notes in Mathematics, Berlin: Springer-Verlag
    • Phelps, R. R. 2001. Lectures on Choquet’s Theorem. Second edn. Lecture Notes in Mathematics, vol. 1757. Berlin: Springer-Verlag.
    • (2001) Lectures on Choquet’s Theorem , vol.1757
    • Phelps, R.R.1
  • 126
    • 0002802366 scopus 로고
    • On the fundamental ideas of measure theory
    • Rokhlin, V. A. 1952. On the fundamental ideas of measure theory. Amer. Math. Soc.Translation, 1952(71), 55.
    • (1952) Amer. Math. Soc.Translation , vol.1952 , Issue.71 , pp. 55
    • Rokhlin, V.A.1
  • 127
    • 0000985844 scopus 로고
    • The structure and properties of invariant measurable partitions
    • Rokhlin, V. A. and Sinai, Y. G. 1961. The structure and properties of invariant measurable partitions. Dokl. Akad. Nauk SSSR, 141, 1038-1041.
    • (1961) Dokl. Akad. Nauk SSSR , vol.141 , pp. 1038-1041
    • Rokhlin, V.A.1    Sinai, Y.G.2
  • 128
    • 0242287406 scopus 로고    scopus 로고
    • A local variational principle for the topological entropy
    • Romagnoli, P.-P. 2003. A local variational principle for the topological entropy. Ergodic Theory Dynam. Systems, 23(5), 1601-1610.
    • (2003) Ergodic Theory Dynam. Systems , vol.23 , Issue.5 , pp. 1601-1610
    • Romagnoli, P.-P.1
  • 129
    • 0004116414 scopus 로고
    • Second edn. McGraw-Hill Series in Higher Mathematics. New York: McGraw-Hill
    • Rudin, W. 1974. Real and Complex Analysis. Second edn. McGraw-Hill Series in Higher Mathematics. New York: McGraw-Hill.
    • (1974) Real and Complex Analysis
    • Rudin, W.1
  • 130
    • 0004057553 scopus 로고
    • Second edn. International Series in Pure and Applied Mathematics. New York: McGraw-Hill
    • Rudin, W. 1991. Functional Analysis. Second edn. International Series in Pure and Applied Mathematics. New York: McGraw-Hill.
    • (1991) Functional Analysis
    • Rudin, W.1
  • 131
    • 51249181713 scopus 로고
    • If a two-point extension of a bernoulli shift has an ergodic square, then it is bernoulli
    • Rudolph, D. J. 1978. If a two-point extension of a Bernoulli shift has an ergodic square, then it is Bernoulli. Israel J. Math., 30(1-2), 159-180.
    • (1978) Israel J. Math , vol.30 , Issue.1-2 , pp. 159-180
    • Rudolph, D.J.1
  • 132
    • 84856043672 scopus 로고
    • A mathematical theory of communication
    • Shannon, C. E. 1948. A Mathematical theory of communication. Bell System Tech., 379-423, 623-656.
    • (1948) Bell System Tech , vol.379-423 , pp. 623-656
    • Shannon, C.E.1
  • 133
    • 84926075593 scopus 로고    scopus 로고
    • Graduate Studies in Mathematics, Providence, RI: American Mathematical Society
    • Shields, P. C. 1996. The Ergodic Theory of Discrete Sample Paths. Graduate Studies in Mathematics, vol. 13. Providence, RI: American Mathematical Society.
    • (1996) The Ergodic Theory of Discrete Sample Paths , vol.13
    • Shields, P.C.1
  • 134
    • 84926113126 scopus 로고
    • Mathematical Expositions, Toronto: University of Toronto Press. Translated by C. Cecilia Krieger
    • Sierpinski, W. 1952. General Topology. Mathematical Expositions, No. 7. Toronto: University of Toronto Press. Translated by C. Cecilia Krieger.
    • (1952) General Topology , Issue.7
    • Sierpinski, W.1
  • 135
    • 0000419815 scopus 로고
    • On the concept of entropy for a dynamic system
    • Sinai, Y. G. 1959. On the concept of entropy for a dynamic system. Dokl. Akad. Nauk SSSR, 124, 768-771.
    • (1959) Dokl. Akad. Nauk SSSR , vol.124 , pp. 768-771
    • Sinai, Y.G.1
  • 136
    • 0037859037 scopus 로고
    • A weak isomorphism of transformations with invariant measure
    • Sinai, Y. G. 1962. A weak isomorphism of transformations with invariant measure. Dokl. Akad. Nauk SSSR, 147, 797-800.
    • (1962) Dokl. Akad. Nauk SSSR , vol.147 , pp. 797-800
    • Sinai, Y.G.1
  • 137
    • 49649134173 scopus 로고
    • On ornstein’s isomorphism theorem for bernoulli shifts
    • Smorodinsky, M. 1972. On Ornstein’s isomorphism theorem for Bernoulli shifts. Advances in Math., 9, 1-9.
    • (1972) Advances in Math , vol.9 , pp. 1-9
    • Smorodinsky, M.1
  • 138
    • 84972541021 scopus 로고
    • A lattice-theoretical fixpoint theorem and its applications
    • Tarski, A. 1955. A lattice-theoretical fixpoint theorem and its applications. Pacific J. Math., 5, 285-309.
    • (1955) Pacific J. Math , vol.5 , pp. 285-309
    • Tarski, A.1
  • 139
    • 84972507756 scopus 로고
    • Some characterizations of normal and perfectly normal spaces
    • Tong, H. 1952. Some characterizations of normal and perfectly normal spaces. Duke Math. J., 19, 289-292.
    • (1952) Duke Math. J. , vol.19 , pp. 289-292
    • Tong, H.1
  • 141
    • 0004008274 scopus 로고
    • Unveranderter Nachdruck der ersten Auflage von 1932. Die Grundlehren der mathematischen Wissenschaften, Band 38. Berlin: Springer-Verlag
    • von Neumann, J. 1968. Mathematische Grundlagender Quantenmechanik. Unveranderter Nachdruck der ersten Auflage von 1932. Die Grundlehren der mathematischen Wissenschaften, Band 38. Berlin: Springer-Verlag.
    • (1968) Mathematische Grundlagender Quantenmechanik
    • Von Neumann, J.1
  • 142
    • 0003904893 scopus 로고
    • Graduate Texts in Mathematics, New York: Springer-Verlag
    • Walters, P. 1982. An Introduction to Ergodic Theory. Graduate Texts in Mathematics, vol. 79. New York: Springer-Verlag.
    • (1982) An Introduction to Ergodic Theory , vol.79
    • Walters, P.1
  • 143
    • 51649149112 scopus 로고
    • Volume growth and entropy
    • Yomdin, Y. 1987. Volume growth and entropy. Israel J. Math., 57(3), 285-300.
    • (1987) Israel J. Math. , vol.57 , Issue.3 , pp. 285-300
    • Yomdin, Y.1
  • 144
    • 84889980482 scopus 로고
    • On the new theory of integration
    • Young, W. H. 1910. On the new theory of integration. Proc. London Math. Soc., 9, 15-50.
    • (1910) Proc. London Math. Soc , vol.9 , pp. 15-50
    • Young, W.H.1
  • 145
    • 0031276041 scopus 로고    scopus 로고
    • A non-shannon-type conditional inequality of information quantities
    • Zhang, Z. and Yeung, R. W. 1997. A non-Shannon-type conditional inequality of information quantities. IEEE Trans. Inform. Theory, 43(6), 1982-1986.
    • (1997) IEEE Trans. Inform. Theory , vol.43 , Issue.6 , pp. 1982-1986
    • Zhang, Z.1    Yeung, R.W.2


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