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october 2013 Recurrence properties of a class of nonautonomous discrete systems
Katsuya Yokoi
Bull. Belg. Math. Soc. Simon Stevin 20(4): 689-705 (october 2013). DOI: 10.36045/bbms/1382448189

Abstract

We study recurrence properties for the nonautonomous discrete system given by a sequence $(f_n)_{n=1}^\infty$ of continuous selfmaps on a compact metric space. In particular, our attention is paid to the case when the sequence $(f_n)_{n=1}^\infty$ converges uniformly to a map $f$ or forms an equicontinuous family. In the first case we investigate the structure and behavior of an $\omega$-limit set of $(f_n)$ by a dynamical property of the limit map $f$. We also present some examples of $(f_n)$ and $f$ on the closed interval: (a) $\omega(x, (f_n)) \smallsetminus \Omega(f)\not=\emptyset$ for some point $x$; or (b) the set of periodic points of $f$ is closed and for some point $x$, $\omega(x, (f_n))$ is infinite. In the second case we create a perturbation of $(f_n)$ whose nonwandering set has small measure.

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Katsuya Yokoi. "Recurrence properties of a class of nonautonomous discrete systems." Bull. Belg. Math. Soc. Simon Stevin 20 (4) 689 - 705, october 2013. https://doi.org/10.36045/bbms/1382448189

Information

Published: october 2013
First available in Project Euclid: 22 October 2013

zbMATH: 1373.37052
MathSciNet: MR3129068
Digital Object Identifier: 10.36045/bbms/1382448189

Subjects:
Primary: 37B20 , 37B55
Secondary: 37E05 , 39A10

Keywords: $\omega$-limit set , Chain recurrent set , nonautonomous

Rights: Copyright © 2013 The Belgian Mathematical Society

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Vol.20 • No. 4 • october 2013
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