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arXiv · 2101.05086

Transitivity in nonautonomous systems

Michaela Mlíchová·Vojtěch Pravec
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Abstract

Let $(X,d)$ be a metric space and $f_{1,\infty}=\{f_n\}_{i=0}^{\infty}$ be a sequence of continuous maps $f_n:X\rightarrow X$ such that $(f_n)$ converges uniformly to a continuous map $f$. We investigate which conditions ensure that the transitivity of functions $f_n$ or the transitivity of the nonautonomous system $(X,f_{1,\infty})$ is inherited to the limit function $f$ and vice versa. Such problem have been studied for instance by A. Fedeli, A. Le Donne or J. Li who give different sufficient condition for inheriting of transitivity from $f_n$ to $f$. In this paper we give a survey of know result relating to this problem and prove new results concerning to transitivity.

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Michaela Mlíchová, Vojtěch Pravec. 2021-01-13. Transitivity in nonautonomous systems. https://arxiv.org/abs/2101.05086

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