Inheriting of chaos in nonautonomous dynamical systems

2013/11/16 by Marta Štefánková, Štefánková, Marta
Computer Science · Mathematics · Physics and Astronomy · #37B05 #37B20 #37B40 #37B55 #54H20 #Chaos control and synchronization #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Nonlinear Dynamics and Pattern Formation

paper · pdf · doi:10.48550/arxiv.1311.4083

openalex publication_date 2013/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider nonautonomous discrete dynamical systems \ f_n\_{n≥ 1}, where every f_n is a surjective continuous map [0,1]→ [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≥ 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 ω-limit sets.

Related

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• Chaotic behavior of uniformly convergent nonautonomous systems with randomly perturbed trajectories
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