Inheriting of chaos in nonautonomous dynamical systems

Marta Štefánková

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arXiv · 1311.4083

Inheriting of chaos in nonautonomous dynamical systems

Marta Štefánková

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Abstract

We consider nonautonomous discrete dynamical systems $\{ f_n\}_{n\ge 1}$, where every $f_n$ is a surjective continuous map $[0,1]\to [0,1]$ such that $f_n$ converges uniformly to a map $f$. We show, among others, that if $f$ is chaotic in the sense of Li and Yorke then the nonautonomous system $ \{ f_n\}_{n\ge 1}$ is Li-Yorke chaotic as well, and that the same is true for distributional chaos. If $f$ has zero topological entropy then the nonautonomous system inherits its infinite $\omega$-limit sets.

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BibTeX RIS

Marta Štefánková. 2013-11-16. Inheriting of chaos in nonautonomous dynamical systems. https://arxiv.org/abs/1311.4083

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