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Journal of Dynamical and Control Systems

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16-04-2015

Specification Property for Topological Spaces

Authors: Sejal Shah, Ruchi Das, Tarun Das

Published in: Journal of Dynamical and Control Systems | Issue 4/2016

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Abstract

We introduce and study here the notion of specification property termed as topological specification property for homeomorphisms on non-compact non-metrizable spaces. We prove that if a self homeomorphism on a totally bounded uniform space is mixing, topologically expansive and topologically shadowing then the map has topological specification property.

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Aoki N, Hiraide K. 1994. Topological theory of dynamical systems. Amsterdam: North-Holland Publishing Co.

Bessa M, Lee M, Wen X. Shadowing, expansiveness and specification for C ¹-conservative systems. To appear in Acta Mathematica Scientia.

Blokh A. Decomposition of dynamical systems on an interval. Russ Math Surv 1983;38:133–134.MathSciNetCrossRefMATH

Bowen R. Periodic points and measures for Axiom A diffeomorphisms. Trans Amer Math Soc 1971;154:377–397.MathSciNetMATH

Bowen R. Periodic orbits for hyperbolic flows. Amer J Math 1972;94:1–30.MathSciNetCrossRefMATH

Ceccherini-Silberstein T, Coornaert M. Sensitivity and Devaneys chaos in uniform spaces. J Dyn Control Syst 2013;19:349–357.MathSciNetCrossRefMATH

Das T, Lee K, Richeson D, Wiseman J. Spectral decomposition for topologically Anosov homeomorphisms on noncompact and non-metrizable spaces. Topology Appl 2013;160:149–158.MathSciNetCrossRefMATH

Dateyama M. The almost weak specification property for ergodic group automorphisms of abelian groups. J. Math. Soc. Japan 1990;42:341–351.MathSciNetCrossRefMATH

Devaney R. An introduction to chaotic dynamical systems. Redwood City: Addison-Wesley; 1989.MATH

10.

Hood B. Topological entropy and uniform spaces. J London Math Soc 1974;8: 633–641.MathSciNetCrossRefMATH

11.

Kelley J. General Topology. D: Van Nostrand Company; 1955.

12.

Li T, Yorke J. Period three implies chaos. Amer Math Monthly 1975;82: 985–992.MathSciNetCrossRefMATH

13.

Kulczycki M, Kwietniak D, Oprocha P. On almost specification and average shadowing properties. Fund. Math 2014;224:241–278.MathSciNetCrossRefMATH

14.

Moriyasu K, Sakai K, Yamamoto K. Regular maps with the specification property. Discrete Contin Dyn Syst 2013;33:2991–3009.MathSciNetCrossRefMATH

15.

Pfister C, Sullivan W. Large deviations estimates for dynamical systems without the specification property. Applications to the β-shifts. Nonlinearity 2005;18:237–261.MathSciNetCrossRefMATH

16.

Pfister C, Sullivan W. On the topological entropy of saturated sets. Ergodic Theory Dynam Systems 2007;27:929–956.MathSciNetCrossRefMATH

17.

Sakai K, Sumi N, Yamamoto K. Diffeomorphisms satisfying the specification property. Proc Amer Math Soc 2010;138:315–321.MathSciNetCrossRefMATH

18.

Schweizer B, Smital J. Measures of chaos and a spectral decomposition of dynamical systems on the interval. Trans Amer Math Soc 1994;344:737–754.MathSciNetCrossRefMATH

19.

Sigmund K. On dynamical systems with the specification property. Trans Amer Math Soc 1974;190:285–299.MathSciNetCrossRefMATH

20.

Sklar A, Smital J. Distributional chaos on compact metric spaces via specification properties. J Math Anal Appl 2000;241:181–188.MathSciNetCrossRefMATH

21.

Taylor J. Chaos in topological spaces. Far East J Dyn Syst 2002;4:115–124.MathSciNetMATH

22.

Wang H, Wang L. The weak specification property and distributional chaos. Nonlinear Anal 2013;91:46–50.MathSciNetCrossRefMATH

23.

Yamamoto K. On the weaker forms of the specification property and their applications. Proc Amer Math Soc 2009;137:3807–3814.MathSciNetCrossRefMATH

Title: Specification Property for Topological Spaces
Authors: Sejal Shah
Ruchi Das
Tarun Das
Publication date: 16-04-2015
Publisher: Springer US
Published in: Journal of Dynamical and Control Systems / Issue 4/2016
Print ISSN: 1079-2724
Electronic ISSN: 1573-8698
DOI: https://doi.org/10.1007/s10883-015-9275-6

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