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Regular and Chaotic Dynamics, 2010, Volume 15, Issue 2-3, Pages 210–221
DOI: https://doi.org/10.1134/S1560354710020097
(Mi rcd489)
 

This article is cited in 2 scientific papers (total in 2 papers)

On the 75th birthday of Professor L.P. Shilnikov

Approximation of entropy on hyperbolic sets for one-dimensional maps and their multidimensional perturbations

Ming-Chia Lia, M. I. Malkinb

a Department of Applied Mathematics, National Chiao Tung University, Hsinchu 300, Taiwan
b Department of Mathematics and Mechanics, Nizhny Novgorod State University, Gagarin Pr. 23, Nizhny Novgorod, 603950 Russia
Citations (2)
Abstract: We consider piecewise monotone (not necessarily, strictly) piecewise $C^2$ maps on the interval with positive topological entropy. For such a map $f$ we prove that its topological entropy $h_{top}(f)$ can be approximated (with any required accuracy) by restriction on a compact strictly $f$-invariant hyperbolic set disjoint from some neighborhood of prescribed set consisting of periodic attractors, nonhyperbolic intervals and endpoints of monotonicity intervals. By using this result we are able to generalize main theorem from [1] on chaotic behavior of multidimensional perturbations of solutions for difference equations which depend on two variables at nonperturbed value of parameter.
Keywords: chaotic dynamics, difference equations, one-dimensional maps, topological entropy, hyperbolic orbits.
Received: 16.02.2010
Accepted: 09.03.2010
Bibliographic databases:
Document Type: Article
MSC: 37D45
Language: English
Citation: Ming-Chia Li, M. I. Malkin, “Approximation of entropy on hyperbolic sets for one-dimensional maps and their multidimensional perturbations”, Regul. Chaotic Dyn., 15:2-3 (2010), 210–221
Citation in format AMSBIB
\Bibitem{LiMal10}
\by Ming-Chia Li, M. I. Malkin
\paper Approximation of entropy on hyperbolic sets for one-dimensional maps and their multidimensional perturbations
\jour Regul. Chaotic Dyn.
\yr 2010
\vol 15
\issue 2-3
\pages 210--221
\mathnet{http://mi.mathnet.ru/rcd489}
\crossref{https://doi.org/10.1134/S1560354710020097}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2644331}
\zmath{https://zbmath.org/?q=an:1213.37058}
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  • This publication is cited in the following 2 articles:
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