메뉴 건너뛰기




Volumn 182, Issue 1, 1996, Pages 105-153

On the dimension of deterministic and random cantor-like sets, symbolic dynamics, and the Eckmann-Ruelle conjecture

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0030353353     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02506387     Document Type: Article
Times cited : (67)

References (47)
  • 1
    • 0000097875 scopus 로고
    • Symbolic dynamics and hyperbolic dynamical systems
    • Alekseyev, V., Jakobson, M.: Symbolic Dynamics and Hyperbolic Dynamical Systems. Phys. Rep. 75, 287-325 (1981)
    • (1981) Phys. Rep. , vol.75 , pp. 287-325
    • Alekseyev, V.1    Jakobson, M.2
  • 2
    • 0041948689 scopus 로고
    • The hausdorff dimension of attractors appearing by Saddle-Node bifurcations
    • Afraimovich, V., Shereshevsky, M.: The Hausdorff Dimension of Attractors Appearing by Saddle-Node Bifurcations. Int. J. Bifurcation and Chaos 1:2, 309-325 (1991)
    • (1991) Int. J. Bifurcation and Chaos , vol.1-2 , pp. 309-325
    • Afraimovich, V.1    Shereshevsky, M.2
  • 3
    • 0040811205 scopus 로고
    • Cantor sets with complicated geometry and modeled by general symbolic dynamics
    • Barreira, L.: Cantor Sets with Complicated Geometry and Modeled by General Symbolic Dynamics. To appear. Random and Computational Dynamics (1995)
    • (1995) Random and Computational Dynamics
    • Barreira, L.1
  • 4
    • 51649148795 scopus 로고
    • Pointwise ergodic theorems for arithmetic sets, with an appendix by J. Bourgain, H. Furstenberg, Y. Katznelson, and D. Ornstein
    • Bourgain, J.: Pointwise Ergodic Theorems for Arithmetic Sets, with an Appendix by J. Bourgain, H. Furstenberg, Y. Katznelson, and D. Ornstein Publ. Math. IHES 69, 5-45 (1989)
    • (1989) Publ. Math. IHES , vol.69 , pp. 5-45
    • Bourgain, J.1
  • 6
    • 0003823726 scopus 로고
    • Equilibrium states and the ergodic theory of anosov diffeomorphisms
    • Berlin-Heidelberg-New York, Springer Verlag
    • Bowen, R.: Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms. Springer Lecture Notes #470, Berlin-Heidelberg-New York, Springer Verlag, 1975
    • (1975) Springer Lecture Notes #470
    • Bowen, R.1
  • 7
    • 51249186941 scopus 로고
    • Hausdorff dimension of Quasi-circles
    • BowBo, R.: Hausdorff Dimension of Quasi-circles. publ. Math. IHES 50, 11-25 (1979)
    • (1979) Publ. Math. IHES , vol.50 , pp. 11-25
    • BowBo, R.1
  • 9
    • 84972072972 scopus 로고
    • The box and Hausdorff dimension of self-affine sets
    • Bedford, T., Urbański, M.: The box and Hausdorff Dimension of Self-Affine Sets. Ergod. Th. and Dynam. Systems 10, 627-644 (1990)
    • (1990) Ergod. Th. and Dynam. Systems , vol.10 , pp. 627-644
    • Bedford, T.1    Urbański, M.2
  • 10
    • 84971851116 scopus 로고
    • Connecting ergodicity and dimension in dynamical systems
    • Cutler, C.D.: Connecting Ergodicity and Dimension in Dynamical Systems. Ergod. Th. and Dynam. Systems 10, 451-462 (1990)
    • (1990) Ergod. Th. and Dynam. Systems , vol.10 , pp. 451-462
    • Cutler, C.D.1
  • 11
    • 0001141522 scopus 로고
    • The dimension spectrum of some dynamical systems
    • Collet, P., Lebowitz, J.L., Porzio, A.: The Dimension Spectrum of Some Dynamical Systems. J. Stat. Physics 47, 609-644 (1987)
    • (1987) J. Stat. Physics , vol.47 , pp. 609-644
    • Collet, P.1    Lebowitz, J.L.2    Porzio, A.3
  • 13
    • 84962991716 scopus 로고
    • Multifractal decomposition of digraph recursive fractals
    • Mauldin, R., Edgar, G.: Multifractal Decomposition of Digraph Recursive fractals. Proc. London Math. Soc. 65, 604-628 (1992)
    • (1992) Proc. London Math. Soc. , vol.65 , pp. 604-628
    • Mauldin, R.1    Edgar, G.2
  • 14
    • 35949018382 scopus 로고
    • Ergodic theory of chaos and strange attractors. 3
    • Eckmann, J.P., Ruelle, D.: Ergodic Theory of Chaos and Strange Attractors. 3. Rev. Mod. Phys. 57, 617-656 (1985)
    • (1985) Rev. Mod. Phys. , vol.57 , pp. 617-656
    • Eckmann, J.P.1    Ruelle, D.2
  • 17
    • 0003418232 scopus 로고
    • Berlin-Heidelberg-New York: Springer Verlag
    • Federer, H.: Geometric Measure Theory. Berlin-Heidelberg-New York: Springer Verlag, 1969
    • (1969) Geometric Measure Theory
    • Federer, H.1
  • 18
    • 0002618708 scopus 로고
    • Potential d'équilibre et capacité des ensembles avec quelques applications à la théorie des fonctions
    • Frostman, O.: Potential d'équilibre et Capacité des Ensembles Avec Quelques Applications à la Théorie des Fonctions. Meddel. Lunds Univ. Math. Sem. 3, 1-118 (1935)
    • (1935) Meddel. Lunds Univ. Math. Sem. , vol.3 , pp. 1-118
    • Frostman, O.1
  • 19
    • 33646727744 scopus 로고
    • Disjointness in Ergodic theory, minimal sets, and a problem in diophantine approximation
    • Furstenberg, H.: Disjointness in Ergodic Theory, Minimal Sets, and a Problem in Diophantine Approximation. Mathematical Systems Theory 1, 1-49 (1967)
    • (1967) Mathematical Systems Theory , vol.1 , pp. 1-49
    • Furstenberg, H.1
  • 20
    • 34250101043 scopus 로고
    • Statistically self-similar fractals
    • Graf, S.: Statistically Self-similar Fractals. Prob. Theory and Related Fields 74, 357-397 (1987)
    • (1987) Prob. Theory and Related Fields , vol.74 , pp. 357-397
    • Graf, S.1
  • 21
    • 0003322695 scopus 로고
    • The exact hausdorff dimension in random recursive constructions. 381
    • Graf, S., Mauldin, D., Williams, S.: The Exact Hausdorff Dimension in Random Recursive Constructions. 381, Mem. Am. Math. Soc. 71, (1988)
    • (1988) Mem. Am. Math. Soc. , vol.71
    • Graf, S.1    Mauldin, D.2    Williams, S.3
  • 23
    • 0346372923 scopus 로고
    • The infinite number of generalized dimensions of fractals and strange attractors
    • Hentschel, H.G.E., Procaccia, I.: The Infinite Number of Generalized Dimensions of Fractals and Strange Attractors. Physica 8D, 435-444 (1983)
    • (1983) Physica , vol.8 D , pp. 435-444
    • Hentschel, H.G.E.1    Procaccia, I.2
  • 24
    • 0040441028 scopus 로고
    • Sur le modèle de turbulence de Benoit Mandelbrot
    • Kahane, J.P.: Sur le Modèle de Turbulence de Benoit Mandelbrot. C.R. Acad. Sci. Paris 278A, 621-623 (1974)
    • (1974) C.R. Acad. Sci. Paris , vol.278 A , pp. 621-623
    • Kahane, J.P.1
  • 26
    • 0008998845 scopus 로고
    • The dimension spectrum of the maximal measure
    • Lopes, A.: The Dimension Spectrum of the Maximal Measure. SIAM J. Math. Analysis 20, 1243-1254 (1989)
    • (1989) SIAM J. Math. Analysis , vol.20 , pp. 1243-1254
    • Lopes, A.1
  • 27
    • 0011829324 scopus 로고
    • Dimension of invariant measures for maps with exponent zero
    • Ledrappier, F., Misiurewicz, M.: Dimension of Invariant Measures for Maps with Exponent Zero. Ergod. Th. and Dynam. Systems 5, 595-610 (1985)
    • (1985) Ergod. Th. and Dynam. Systems , vol.5 , pp. 595-610
    • Ledrappier, F.1    Misiurewicz, M.2
  • 28
    • 0001048955 scopus 로고
    • The metric entropy of diffeomorphisms. Part II
    • Ledrappier, F., Young, L.S.: The Metric Entropy of Diffeomorphisms. Part II. Ann. of Math. 122, 540-574 (1985)
    • (1985) Ann. of Math. , vol.122 , pp. 540-574
    • Ledrappier, F.1    Young, L.S.2
  • 29
    • 84972500327 scopus 로고
    • The Hausdorff dimension of general Sierpiński carpets
    • McMullen, C.: The Hausdorff Dimension of General Sierpiński Carpets. Nagoya Math. J. 96, 1-9 (1984)
    • (1984) Nagoya Math. J. , vol.96 , pp. 1-9
    • McMullen, C.1
  • 30
    • 84966230972 scopus 로고
    • Hausdorff dimension in graph directed constructions
    • Mauldin, R., Williams, S.: Hausdorff Dimension in Graph Directed Constructions. Trans. AMS 309:2, 811-829 (1988)
    • (1988) Trans. AMS , vol.309 , Issue.2 , pp. 811-829
    • Mauldin, R.1    Williams, S.2
  • 31
    • 0006799223 scopus 로고
    • Random geometric constructions: Asymptotic, geometric and asymptotic properties
    • Mauldin, R., Williams, S.: Random Geometric Constructions: Asymptotic, Geometric and Asymptotic Properties. Trans. Am. Math. Soc. 295, 325-346 (1986)
    • (1986) Trans. Am. Math. Soc. , vol.295 , pp. 325-346
    • Mauldin, R.1    Williams, S.2
  • 32
    • 0039771567 scopus 로고
    • Additive functions of intervals and Hausdorff dimension
    • Moran, P.: Additive Functions of Intervals and Hausdorff Dimension. Proc. Camb. Phil. Society 42, 15-23 (1946)
    • (1946) Proc. Camb. Phil. Society , vol.42 , pp. 15-23
    • Moran, P.1
  • 33
    • 0041034894 scopus 로고
    • Lyapunov partition functions for the dimensions of chaotic sets
    • Ott, E., Sauer, T., Yorke, J.: Lyapunov Partition Functions for the Dimensions of Chaotic Sets. no 9, Phys. Rev. A 39, 4212-4222 (1989)
    • (1989) Phys. Rev. A , vol.39 , Issue.9 , pp. 4212-4222
    • Ott, E.1    Sauer, T.2    Yorke, J.3
  • 34
    • 0000271607 scopus 로고
    • Zeta functions and the periodic orbit structures of hyperbolic dynamics
    • Parry, W., Pollicott, W.: Zeta Functions and the Periodic Orbit Structures of Hyperbolic Dynamics. Astérisque 187-188, (1990)
    • (1990) Astérisque , vol.187-188
    • Parry, W.1    Pollicott, W.2
  • 35
    • 0037565847 scopus 로고
    • On the dimension of deterministic and random Cantor-like sets
    • Pesin, Y., Weiss, H.: On the Dimension of Deterministic and Random Cantor-like Sets. Math. Res. Lett. 1, 519-529 (1994)
    • (1994) Math. Res. Lett. , vol.1 , pp. 519-529
    • Pesin, Y.1    Weiss, H.2
  • 38
    • 0000690674 scopus 로고
    • On Hausdorff dimension of some fractal sets
    • Przytycki, F., Urbański, M.: On Hausdorff Dimension of Some Fractal Sets. Studia Mathematica 93, 155-186 (1989)
    • (1989) Studia Mathematica , vol.93 , pp. 155-186
    • Przytycki, F.1    Urbański, M.2
  • 41
    • 0039256285 scopus 로고
    • On the hausdorff dimension of a class of non-self-similar fractals
    • Shereshevsky, M.: On the Hausdorff Dimension of a Class of Non-Self-Similar Fractals. Math. Notes 50, no. 5, 1184-1187 1991
    • (1991) Math. Notes , vol.50 , Issue.5 , pp. 1184-1187
    • Shereshevsky, M.1
  • 43
    • 84966226777 scopus 로고
    • On hausdorff dimension of recurrent net fractals
    • Stella, S.: On Hausdorff Dimension of Recurrent Net Fractals. Proc. Am. Math. Soc. 116, 389-400 (1992)
    • (1992) Proc. Am. Math. Soc. , vol.116 , pp. 389-400
    • Stella, S.1
  • 44
    • 84956256298 scopus 로고
    • Dimension, entropy, and lyapunov exponents
    • Young, L.S.: Dimension, Entropy, and Lyapunov Exponents. Ergod. Th. and Dynam. Systems 2, 109-124 (1982)
    • (1982) Ergod. Th. and Dynam. Systems , vol.2 , pp. 109-124
    • Young, L.S.1
  • 46
    • 33845991986 scopus 로고
    • Subshifts of finite type and Sophie systems
    • Weiss, B.: Subshifts of Finite Type and Sophie Systems. Monatschefte für Mathematik 77, 462-474 (1973)
    • (1973) Monatschefte für Mathematik , vol.77 , pp. 462-474
    • Weiss, B.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.