On the sensitivities dependence in non-autonomous dynamical systems

2016/01/30 by Chengyu Yang, Zhiming Li, Yang, Chengyu +1
Computer Science · Mathematics · Physics and Astronomy · #37B55 #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Nonlinear Dynamics and Pattern Formation #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1602.00075

openalex publication_date 2016/01/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For discrete autonomous dynamical systems (ADS) (X, d, f), it was found that in the three conditions defining Devaney chaos, topological transitivity and dense periodic points together imply sensitive dependence on initial condition(Banks, Brooks, Cairns, Davis and Stacey, 1992). In this paper, the result of Banks et al. is generalized to a class of the non-autonomous dynamical systems (NADS) (X,f_1,∞). Also, by the studying of NADS over their iterated systems (X,f_1,∞^[k]), we know that for two sensitive NADS, the one which preserve sensitive in its any times iterated systems is more sensitive than the one not. In this case, several sufficient conditions ensuring two kinds of sensitivities are preserved under the arbitrary number of iterations of certain NADS are given.

Related

• Sensitivity, transitivity and chaos in non-autonomous discrete systems
• Sensitive dependence and dense perodic points
• Dynamics of multi-sensitive non-autonomous systems with respect to a vector
• Induced Dynamics of Non-Autonomous Discrete Dynamical Systems
• Auslander-Yorke Dichotomy and Its Generalizations for Non-Autonomous Dynamical Systems