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Izv. Akad. Nauk SSSR Ser. Mat., 1971, Volume 35, Issue 2, Pages 324–366 (Mi izv1975)  

This article is cited in 32 scientific papers (total in 32 papers)

On the relations among various entropy characteristics of dynamical systems

E. I. Dinaburg


Abstract: This paper deals with the relation between topological entropy and $\varepsilon$-entropy of the space of segments of trajectories of dynamical systems, as well as the relation between topological and metrical entropies. The results obtained are applied to some classical dynamical systems.

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English version:
Mathematics of the USSR-Izvestiya, 1971, 5:2, 337–378

Bibliographic databases:

UDC: 513.88
MSC: 28A65, 54H20, 58F99
Received: 08.05.1970

Citation: E. I. Dinaburg, “On the relations among various entropy characteristics of dynamical systems”, Izv. Akad. Nauk SSSR Ser. Mat., 35:2 (1971), 324–366; Math. USSR-Izv., 5:2 (1971), 337–378

Citation in format AMSBIB
\Bibitem{Din71}
\by E.~I.~Dinaburg
\paper On the relations among various entropy characteristics of dynamical systems
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1971
\vol 35
\issue 2
\pages 324--366
\mathnet{http://mi.mathnet.ru/izv1975}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=286091}
\zmath{https://zbmath.org/?q=an:0216.44704}
\transl
\jour Math. USSR-Izv.
\yr 1971
\vol 5
\issue 2
\pages 337--378
\crossref{https://doi.org/10.1070/IM1971v005n02ABEH001050}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Ya. G. Sinai, “Gibbs measures in ergodic theory”, Russian Math. Surveys, 27:4 (1972), 21–69  mathnet  crossref  mathscinet  zmath
    2. A. A. Brudno, “Simvolicheskaya dinamika i entropiya”, UMN, 32:3(195) (1977), 180–180  mathnet  mathscinet  zmath
    3. Lai-Sang Young, “Entropy of continuous flows on compact 2-manifolds”, Topology, 16:4 (1977), 469  crossref
    4. A. Katok, “Lyapunov exponents, entropy and periodic orbits for diffeomorphisms”, Publications Mathématiques de l’Institut des Hautes Études Scientifiques, 51:1 (1980), 137  crossref  mathscinet  zmath
    5. A. A. Simonov, “Measures with maximal entropy for piecewise monotone transformations of an interval”, Russian Math. Surveys, 35:5 (1980), 273–274  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    6. Anthony Manning, “A relation between Lyapunov exponents, Hausdorff dimension and entropy”, Ergod Th Dynam Sys, 1:4 (1981)  crossref  mathscinet
    7. A. Katok, “Entropy and closed geodesies”, Ergod Th Dynam Sys, 2:3-4 (1982)  crossref  mathscinet
    8. M. Ju. Ljubich, “Entropy properties of rational endomorphisms of the Riemann sphere”, Ergod Th Dynam Sys, 3:3 (1983)  crossref  mathscinet
    9. Ya. B. Pesin, B. S. Pitskel', “Topological pressure and the variational principle for noncompact sets”, Funct. Anal. Appl., 18:4 (1984), 307–318  mathnet  crossref  mathscinet  zmath  isi
    10. Y. Takahashi, Y. Oono, “Towards the Statistical Mechanics of Chaos”, Progress of Theoretical Physics, 71:4 (1984), 851  crossref
    11. Y. Yomdin, “Volume growth and entropy”, Isr J Math, 57:3 (1987), 285  crossref  mathscinet  zmath  isi
    12. Gonzalo Contreras, “Regularity of topological and metric entropy of hyperbolic flows”, Math Z, 210:1 (1992), 97  crossref  mathscinet  zmath  isi
    13. Gabriel P. Paternain, “On the topology of manifolds with completely integrable geodesic flows”, Ergod Th Dynam Sys, 12:1 (1992)  crossref  mathscinet
    14. Gabriel P. Paternain, “Multiplicity two actions and loop space homology”, Ergod Th Dynam Sys, 13:1 (1993)  crossref  mathscinet
    15. Gabriel P. Paternain, “On the topology of manifolds with completely integrable geodesic flows II”, Journal of Geometry and Physics, 13:3 (1994), 289  crossref
    16. Gérard Besson, Gilles Courtois, Sylvestre Gallot, “Minimal entropy and Mostow's rigidity theorems”, Ergod Th Dynam Sys, 16:4 (1996)  crossref
    17. Arnold J. Mandell, Karen A. Selz, “Entropy conservation as h[sub T[sub μ]]≈λ̄[sub μ][sup +]d[sub μ] in neurobiological dynamical systems”, Chaos, 7:1 (1997), 67  crossref  mathscinet  zmath  isi
    18. I. K. Babenko, “Topological entropy of geodesic flows on simply connected manifolds, and related topics”, Izv. Math., 61:3 (1997), 517–535  mathnet  crossref  crossref  mathscinet  zmath  isi
    19. M. I. Voinova, L. S. Efremova, “Dynamics of elementary maps of dendrites”, Math. Notes, 63:2 (1998), 161–171  mathnet  crossref  crossref  mathscinet  zmath  isi
    20. A. V. Bolsinov, I. A. Taimanov, “Integrable Geodesic Flows on the Suspensions of Toric Automorphisms”, Proc. Steklov Inst. Math., 231 (2000), 42–58  mathnet  mathscinet  zmath
    21. Paternain G.P., “Differentiable structures with zero entropy on simply connected 4-manifolds”, Boletim da Sociedade Brasileira de Matematica, 31:1 (2000), 1–8  crossref  isi
    22. Paternain G.P., Petean J., “Entropy and collapsing of compact complex surfaces”, Proceedings of the London Mathematical Society, 89:Part 3 (2004), 763–786  crossref  isi  elib
    23. Osin D.V., “Algebraic entropy of elementary amenable groups”, Geometriae Dedicata, 107:1 (2004), 133–151  crossref  isi  elib
    24. Bolsinov A.V., “Integrable geodesic flows on Riemannian manifolds: Construction and obstructions”, Proceedings of the Workshop on Contemporary Geometry and Related Topics, 2004, 57–103  isi
    25. Fei Liu, Xiang Zhang, “Integrable Natural Hamiltonian Systems on the Suspensions of Toric Automorphism”, Qual Th Dyn Syst, 2010  crossref
    26. Gonzalo Contreras, “Geodesic flows with positive topological entropy, twist maps and hyperbolicity”, Ann of Math, 172:2 (2010), 761  crossref
    27. JOSÉ BARBOSA GOMES, RAFAEL O. RUGGIERO, “On Finsler surfaces without conjugate points”, Ergod. Th. Dynam. Sys, 2012, 1  crossref
    28. Fritz Colonius, Christoph Kawan, Girish Nair, “A note on topological feedback entropy and invariance entropy”, Systems & Control Letters, 62:5 (2013), 377  crossref
    29. Xiaoxia Huang, Liya Huang, Tzyy-Ping Jung, Chung-Kuan Cheng, A.J.. Mandell, “Intrinsic Mode Functions Locate Implicit Turbulent Attractors in Time in Frontal Lobe MEG Recordings”, Neuroscience, 2014  crossref
    30. J.P.hilipp Schröder, “Ergodicity and topological entropy of geodesic flows on surfaces”, JMD, 9:01 (2015), 147  crossref
    31. S. V. Bolotin, V. V. Kozlov, “Topology, singularities and integrability in Hamiltonian systems with two degrees of freedom”, Izv. Math., 81:4 (2017), 671–687  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    32. B. Ya. Ryabko, “Information-theoretic approach to estimating the capacity of distributed memory systems”, Problems Inform. Transmission, 54:2 (2018), 191–198  mathnet  crossref  isi  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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