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Volumn 16, Issue 7, 2014, Pages 3732-3753

On the connections of generalized entropies with Shannon and Kolmogorov-Sinai entropies

Author keywords

Dynamical entropy; Kolmogorov Sinai entropy

Indexed keywords


EID: 84933533614     PISSN: None     EISSN: 10994300     Source Type: Journal    
DOI: 10.3390/e16073732     Document Type: Article
Times cited : (15)

References (33)
  • 2
    • 0003406478 scopus 로고    scopus 로고
    • Introduction to the Modern Theory of Dynamical Systems
    • Cambridge University Press: New York, NY, USA
    • Katok, A.; Hasselblatt, B. Introduction to the Modern Theory of Dynamical Systems; Cambridge University Press: New York, NY, USA, 1997.
    • (1997)
    • Katok, A.1    Hasselblatt, B.2
  • 3
    • 0000203008 scopus 로고
    • + action on a compact space
    • + action on a compact space. Astérisque 1976, 40, 147-157.
    • (1976) Astérisque , vol.40 , pp. 147-157
    • Misiurewicz, M.1
  • 4
    • 84940644968 scopus 로고
    • A mathematical theory of communication
    • Shannon, C.E. A mathematical theory of communication. Bell Syst. Tech. J. 1948, 27, 379-423, 623-656.
    • (1948) Bell Syst. Tech. J. , vol.27
    • Shannon, C.E.1
  • 5
    • 0002408684 scopus 로고
    • On measures of entropy and informatio
    • Statistical Laboratory of the University of California, Berkeley, CA, USA, 20 June-30 July, University of California Press, Berkeley, CA, USA 1961
    • Rényi, A. On measures of entropy and information. In Proceedings of the 4th Berkeley Symposium on Mathematical Statistics and Probability, Statistical Laboratory of the University of California, Berkeley, CA, USA, 20 June-30 July 1960; University of California Press: Berkeley, CA, USA, 1961; Volume 1, pp. 547-561.
    • (1960) Proceedings of the 4th Berkeley Symposium on Mathematical Statistics and Probability , vol.1 , pp. 547-561
    • Rényi, A.1
  • 6
    • 0000242156 scopus 로고
    • Information-theoretical considerations on estimation problems
    • Arimoto, S. Information-theoretical considerations on estimation problems. Inf. Control 1971, 19, 181-194.
    • (1971) Inf. Control , vol.19 , pp. 181-194
    • Arimoto, S.1
  • 7
    • 77954596738 scopus 로고    scopus 로고
    • Rényi Information Dimension: Fundamental Limits of Almost Lossless Analog Compression
    • Wu, Y.; Verdú, S. Rényi Information Dimension: Fundamental Limits of Almost Lossless Analog Compression. IEEE Trans. Inf. Theory 2010, 56, 3721-3748.
    • (2010) IEEE Trans. Inf. Theory , vol.56 , pp. 3721-3748
    • Wu, Y.1    Verdú, S.2
  • 8
    • 54749100076 scopus 로고    scopus 로고
    • Axiomatic characterization of information measures
    • Csiszár, I. Axiomatic characterization of information measures. Entropy 2008, 10, 261-273.
    • (2008) Entropy , vol.10 , pp. 261-273
    • Csiszár, I.1
  • 9
    • 84933504371 scopus 로고
    • On entropy-like invariants for dynamical systems
    • De Paly, T. On entropy-like invariants for dynamical systems. Z. Anal. Anwend. 1982, 1, 69-79.
    • (1982) Z. Anal. Anwend. , vol.1 , pp. 69-79
    • De Paly, T.1
  • 10
    • 84933537755 scopus 로고
    • On a class of generalized K-entropies and Bernoulli shifts
    • De Paly, T. On a class of generalized K-entropies and Bernoulli shifts. Z. Anal. Anwend. 1982, 1, 87-96.
    • (1982) Z. Anal. Anwend. , vol.1 , pp. 87-96
    • De Paly, T.1
  • 11
    • 4243243202 scopus 로고
    • Estimation of the Kolmogorov entropy from a chaotic signal
    • Grassberger, P.; Procaccia, I. Estimation of the Kolmogorov entropy from a chaotic signal. Phys. Rev. A 1983, 28, 2591-2593.
    • (1983) Phys. Rev. A , vol.28 , pp. 2591-2593
    • Grassberger, P.1    Procaccia, I.2
  • 12
    • 0005178883 scopus 로고    scopus 로고
    • Generalized entropies: Rényi and correlation integral approach
    • Takens, F.; Verbitski, E. Generalized entropies: Rényi and correlation integral approach. Nonlinearity 1998, 11, 771-782.
    • (1998) Nonlinearity , vol.11 , pp. 771-782
    • Takens, F.1    Verbitski, E.2
  • 13
    • 0142230877 scopus 로고    scopus 로고
    • Rényi entropies of aperiodic dynamical systems
    • Takens, F.; Verbitski, E. Rényi entropies of aperiodic dynamical systems. Isr. J. Math. 2002, 127, 279-302.
    • (2002) Isr. J. Math. , vol.127 , pp. 279-302
    • Takens, F.1    Verbitski, E.2
  • 14
    • 68649092244 scopus 로고    scopus 로고
    • A generalized Kolmogorov-Sinai-like entropy under Markov shifts in symbolic dynamics
    • Liu, Q.; Cao, K.-F.; Peng, S.-L. A generalized Kolmogorov-Sinai-like entropy under Markov shifts in symbolic dynamics. Physica A 2009, 388, 4333-4344.
    • (2009) Physica A , vol.388 , pp. 4333-4344
    • Liu, Q.1    Cao, K.-F.2    Peng, S.-L.3
  • 15
    • 0030501348 scopus 로고    scopus 로고
    • Invariant of dynamical systems: A generalized entropy
    • Mesón, A.M.; Vericat, F. Invariant of dynamical systems: A generalized entropy. J. Math. Phys. 1996, 37, 4480-4483.
    • (1996) J. Math. Phys. , vol.37 , pp. 4480-4483
    • Mesón, A.M.1    Vericat, F.2
  • 16
    • 0035981896 scopus 로고    scopus 로고
    • On the Kolmogorov-like generalization of Tsallis entropy, correlation entropies and multifractal analysis
    • Mesón, A.M.; Vericat, F. On the Kolmogorov-like generalization of Tsallis entropy, correlation entropies and multifractal analysis. J. Math. Phys. 2002, 43, 904-918.
    • (2002) J. Math. Phys. , vol.43 , pp. 904-918
    • Mesón, A.M.1    Vericat, F.2
  • 18
    • 2342551100 scopus 로고    scopus 로고
    • Tsallis entropy: How unique?
    • Abe, S. Tsallis entropy: How unique? Contin. Mech. Thermodyn. 2004, 16, 237-244.
    • (2004) Contin. Mech. Thermodyn. , vol.16 , pp. 237-244
    • Abe, S.1
  • 19
    • 33644630453 scopus 로고    scopus 로고
    • Information theoretical properties of Tsallis entropies
    • Furuichi, S. Information theoretical properties of Tsallis entropies. J. Math. Phys. 2006, 47, 023302.
    • (2006) J. Math. Phys. , vol.47 , pp. 023302
    • Furuichi, S.1
  • 20
    • 33646516485 scopus 로고
    • Possible generalization of Boltzmann-Gibbs statistics
    • Tsallis, C. Possible generalization of Boltzmann-Gibbs statistics. J. Stat. Phys. 1988, 52, 479-487.
    • (1988) J. Stat. Phys. , vol.52 , pp. 479-487
    • Tsallis, C.1
  • 21
    • 0036489566 scopus 로고    scopus 로고
    • Entropic nonextensivity: A possible measure of complexity
    • Tsallis, C. Entropic nonextensivity: A possible measure of complexity. Chaos Solitons Fractals 2002, 13, 371-391.
    • (2002) Chaos Solitons Fractals , vol.13 , pp. 371-391
    • Tsallis, C.1
  • 22
    • 0042128380 scopus 로고    scopus 로고
    • Power-law sensitivity to initial conditions-New entropic representation
    • Tsallis, C.; Plastino, A.R.; Zheng,W.-M. Power-law sensitivity to initial conditions-New entropic representation. Chaos Solitons Fractals 1997, 8, 885-891.
    • (1997) Chaos Solitons Fractals , vol.8 , pp. 885-891
    • Tsallis, C.1    Plastino, A.R.2    Zheng, W.-M.3
  • 23
    • 58449115902 scopus 로고    scopus 로고
    • Entropy is the only finitely observable invariant
    • Ornstein, D.S.; Weiss, B. Entropy is the only finitely observable invariant. J. Mod. Dyn. 2007, 1, 93-105.
    • (2007) J. Mod. Dyn. , vol.1 , pp. 93-105
    • Ornstein, D.S.1    Weiss, B.2
  • 25
    • 0142233527 scopus 로고    scopus 로고
    • American Mathematical Society: Providence, RI, USA
    • Weiss, B. Single Orbit Dynamics; American Mathematical Society: Providence, RI, USA, 2000.
    • (2000) Single Orbit Dynamics
    • Weiss, B.1
  • 26
    • 0039018282 scopus 로고
    • Ph.D. Thesis, University of North Carolina, Chapel Hill, NC, USA
    • Blume, F. The Rate of Entropy Convergence. Ph.D. Thesis, University of North Carolina, Chapel Hill, NC, USA, 1995.
    • (1995) The Rate of Entropy Convergence
    • Blume, F.1
  • 27
    • 0031483723 scopus 로고    scopus 로고
    • Possible rates of entropy convergence
    • Blume, F. Possible rates of entropy convergence. Ergod. Theory Dyn. Syst. 1997, 17, 45-70.
    • (1997) Ergod. Theory Dyn. Syst. , vol.17 , pp. 45-70
    • Blume, F.1
  • 28
    • 0346913337 scopus 로고    scopus 로고
    • Global and local complexity in weakly chaotic dynamical systems
    • Galatolo, S. Global and local complexity in weakly chaotic dynamical systems. Discret. Contin. Dyn. Syst. 2003, 9, 1607-1624.
    • (2003) Discret. Contin. Dyn. Syst. , vol.9 , pp. 1607-1624
    • Galatolo, S.1
  • 29
    • 33847702819 scopus 로고    scopus 로고
    • Entropy dimensions and a class of constructive examples
    • Ferenczi, S.; Park, K.K. Entropy dimensions and a class of constructive examples. Discret. Contin. Dyn. Syst. 2007, 17, 133-141.
    • (2007) Discret. Contin. Dyn. Syst. , vol.17 , pp. 133-141
    • Ferenczi, S.1    Park, K.K.2
  • 31
    • 3042960281 scopus 로고
    • Sub-additive functions
    • Rosenbaum, R.A. Sub-additive functions. Duke Math. J. 1950, 17, 227-247.
    • (1950) Duke Math. J. , vol.17 , pp. 227-247
    • Rosenbaum, R.A.1
  • 32
    • 33846073996 scopus 로고    scopus 로고
    • Rokhlin's Lemma for non-invertible maps
    • Heinemann, S.-M.; Schmitt, O. Rokhlin's Lemma for non-invertible maps. Dyn. Syst. Appl. 2001, 10, 201-214.
    • (2001) Dyn. Syst. Appl. , vol.10 , pp. 201-214
    • Heinemann, S.-M.1    Schmitt, O.2
  • 33
    • 67649301813 scopus 로고
    • Weak isomorphism of transformation with an invariant measure
    • Sinai, Y.G. Weak isomorphism of transformation with an invariant measure. Sov. Math. 1962, 3, 1725-1729.
    • (1962) Sov. Math. , vol.3 , pp. 1725-1729
    • Sinai, Y.G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.