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Properties of invariant measures in dynamical systems with the shadowing property.(English)Zbl 1397.37093

Summary: For dynamical systems with the shadowing property, we provide a method of approximation of invariant measures by ergodic measures supported on odometers and their almost one-to-one extensions. For a topologically transitive system with the shadowing property, we show that ergodic measures supported on odometers are dense in the space of invariant measures, and then ergodic measures are generic in the space of invariant measures. We also show that for every \(c\geq 0\) and \(\varepsilon>0\) the collection of ergodic measures (supported on almost one-to-one extensions of odometers) with entropy between \(c\) and \(c+\varepsilon\) is dense in the space of invariant measures with entropy at least \(c\). Moreover, if in addition the entropy function is upper semi-continuous, then, for every \(c\geq 0\), ergodic measures with entropy \(c\) are generic in the space of invariant measures with entropy at least \(c\).

MSC:

37M25 Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy, etc.)
37B05 Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.)
37C50 Approximate trajectories (pseudotrajectories, shadowing, etc.) in smooth dynamics
37A25 Ergodicity, mixing, rates of mixing

Cite

References:

[1]Aoki, N. and Hiraide, K.. Topological theory of dynamical systems. Recent Advances. North-Holland Publishing, Amsterdam, 1994. ·Zbl 0798.54047
[2]Bowen, R., Periodic points and measures for Axiom A diffeomorphisms, Trans. Amer. Math. Soc., 154, 377-397, (1971) ·Zbl 0212.29103
[3]Bowen, R., Entropy-expansive maps, Trans. Amer. Math. Soc., 164, 323-331, (1972) ·Zbl 0229.28011 ·doi:10.1090/S0002-9947-1972-0285689-X
[4]Bowen, R., 𝜔-limit sets for Axiom A diffeomorphisms, J. Differential Equations, 18, 333-339, (1975) ·Zbl 0315.58019 ·doi:10.1016/0022-0396(75)90065-0
[5]Brucks, K. M. and Bruin, H.. Topics from One-dimensional Dynamics. Cambridge University Press, Cambridge, 2004. doi:10.1017/CBO9780511617171 ·Zbl 1074.37022
[6]Comman, H.. Criteria for the density of the graph of the entropy map restricted to ergodic states. Ergod. Th. & Dynam. Sys. published online, doi:10.107/etds/2015.72. ·Zbl 1375.37018
[7]Delahaye, J.-P., Fonctions admettant des cycles d’ordre n’importe quelle puissance de 2 et aucun autre cycle. (French) [Functions admitting cycles of any power of 2 and no other cycle], C. R. Acad. Sci. Paris Sér. A-B, 291, 4, A323-A325, (1980) ·Zbl 0455.65084
[8]Denker, M., Grillenberger, C. and Sigmund, K.. Ergodic Theory on Compact Spaces. Springer, Berlin, 1976. doi:10.1007/BFb0082364 ·Zbl 0328.28008
[9]Downarowicz, T.. Survey of odometers and Toeplitz flows. Algebraic and Topological Dynamics. American Mathematics Society, Providence, RI, 2005, p. 737. ·Zbl 1096.37002
[10]Dudley, R., Real Analysis and Probability, (2002), Cambridge University Press: Cambridge University Press, Cambridge ·Zbl 1023.60001 ·doi:10.1017/CBO9780511755347
[11]Dong, Y., Oprocha, P. and Tian, X.. On the irregular points for systems with the shadowing property.Ergod. Th. & Dynam. Sys., to appear. ·Zbl 1397.37009
[12]Eizenberg, A., Kifer, Y. and Weiss, B.. Large deviations for ℤd-actions. Commun. Math. Phys.164 (1994), 433-454. doi:10.1007/BF02101485 ·Zbl 0841.60086
[13]Gurevič, B. M.. Topological entropy of a countable Markov chain. Dokl. Akad. Nauk SSSR187 (1969), 715-718 (Russian); English trans.Soviet Math. Dokl.10 (1969), 911-915. ·Zbl 0194.49602
[14]Haraczyk, G., Kwietniak, D. and Oprocha, P.. Topological structure and entropy of mixing graph maps. Ergod. Th. & Dynam. Sys.34 (2014), 1587-1614. doi:10.1017/etds.2013.6 ·Zbl 1351.37174
[15]Israel, R. B. and Phelps, R. R.. Some convexity questions arising in statistical mechanics. Math. Scand.54 (1984), 133-156. doi:10.7146/math.scand.a-12048 ·Zbl 0605.46013
[16]Kitchens, B. P., Symbolic dynamics, One-sided, Two-sided and Countable State Markov Shifts, (1998), Springer: Springer, Berlin ·Zbl 0892.58020
[17]Kuchta, M., Shadowing property of continuous maps with zero topological entropy, Proc. Amer. Math. Soc., 119, 641-648, (1993) ·Zbl 0827.54025 ·doi:10.1090/S0002-9939-1993-1165058-X
[18]Kurka, P., Topological and symbolic dynamics, Cours Spécialisés [Specialized Courses], 11, (2003), Société Mathématique de France: Société Mathématique de France, Paris ·Zbl 1038.37011
[19]Kwietniak, D., Łacka, M. and Oprocha, P.. A panorama of specification-like properties and their consequences. Dynamics and Numbers. American Mathematical Society, Providence, RI, 2016, pp. 155-186. doi:10.1090/conm/669/13428 ·Zbl 1376.37024
[20]Li, J. and Oprocha, P.. Shadowing property, weak mixing and regular recurrence. J. Dynam. Differential Equations25 (2013), 1233-1249. doi:10.1007/s10884-013-9338-x ·Zbl 1294.37006
[21]Lind, D. and Marcus, B.. An Introduction to Symbolic Dynamics and Coding. Cambridge University Press, Cambridge, 1995. doi:10.1017/CBO9780511626302 ·Zbl 1106.37301
[22]Misiurewicz, M., Diffeomorphism without any measure with maximal entropy, Bull. Acad. Pol. Sci., 21, 903-910, (1973) ·Zbl 0272.28013
[23]Moothathu, T. K. S., Implications of pseudo-orbit tracing property for continuous maps on compacta, Topol. Appl., 158, 2232-2239, (2011) ·Zbl 1235.54018 ·doi:10.1016/j.topol.2011.07.016
[24]Moothathu, T. K. S. and Oprocha, P.. Shadowing, entropy and minimal subsystems. Monatsh. Math.172 (2013), 357-378. doi:10.1007/s00605-013-0504-3 ·Zbl 1285.37002
[25]Paul, M. E., Construction of almost automorphic symbolic minimal flows, Gen. Topol. Appl., 6, 45-56, (1976) ·Zbl 0341.54054 ·doi:10.1016/0016-660X(76)90007-6
[26]Pfister, C.-E. and Sullivan, W. G.. Large deviations estimates for dynamical systems without the specification property. Applications to the 𝛽-shifts. Nonlinearity18 (2005), 237-261. doi:10.1088/0951-7715/18/1/013 ·Zbl 1069.60029
[27]Richeson, D. and Wiseman, J.. Chain recurrence rates and topological entropy. Topol. Appl.156(2) (2008), 251-261. doi:10.1016/j.topol.2008.07.005 ·Zbl 1151.37304
[28]Ruelle, D., Statistical mechanics on a compact set with ℤ action satisfying expansiveness and specification, Trans. Amer. Math. Soc., 185, 237-251, (1973) ·Zbl 0278.28012 ·doi:10.2307/1996437
[29]Ruette, S., On the Vere-Jones classification and existence of maximal measures for countable topological Markov chains, Pacific J. Math., 209, 366-380, (2003) ·Zbl 1055.37020 ·doi:10.2140/pjm.2003.209.365
[30]Ruette, S.. Chaos on the interval — a survey of relationship between the various kinds of chaos for continuous interval maps. University Lecture Series, American Mathematical Society, to appear. ·Zbl 1417.37029
[31]Salama, I. A.. On the recurrence of countable topological Markov chains. Symbolic Dynamics and Its Applications (New Haven, CT, 1991). American Mathematical Society, Providence, RI, 1992, pp. 349-360. doi:10.1090/conm/135/1185102 ·Zbl 0801.54032
[32]Sigmund, K., Generic properties of invariant measures for Axiom A diffeomorphisms, Invent. Math., 11, 99-109, (1970) ·Zbl 0193.35502 ·doi:10.1007/BF01404606
[33]Sigmund, K., On dynamical systems with the specification property, Trans. Amer. Math. Soc., 190, 285-299, (1974) ·Zbl 0286.28010 ·doi:10.1090/S0002-9947-1974-0352411-X
[34]Vere-Jones, D., Geometric ergodicity in denumerable Markov chains, Quart. J. Math. Oxford Ser., 13, 7-28, (1962) ·Zbl 0104.11805 ·doi:10.1093/qmath/13.1.7
[35]Walters, P.. On the pseudo-orbit tracing property and its relationship to stability. The Structure of Attractors in Dynamical Systems (Proc. Conf., North Dakota State University, Fargo, ND, 1977). Springer, Berlin, 1978, pp. 231-244. doi:10.1007/BFb0101795 ·Zbl 0403.58019
[36]Walters, P., An Introduction to Ergodic Theory, (2001), Springer: Springer, Berlin
[37]Williams, S., Toeplitz minimal flows which are not uniquely ergodic, Z. Wahrsch. Verw. Gebiete, 67, 95-107, (1984) ·Zbl 0584.28007 ·doi:10.1007/BF00534085
[38]Coven, E. M., Kan, I. and Yorke, J. A.. Pseudo-orbit shadowing in the family of tent maps. Trans. Amer. Math. Soc.308 (1988), 227-241. doi:10.1090/S0002-9947-1988-0946440-2 ·Zbl 0651.58032
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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