Year: 2016
Type: preprint
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) $(X,f_{1,\infty})$. Also, by the studying of NADS over their iterated systems $(X,f_{1,\infty}^{[k]})$, 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.
Source: arXiv (Cornell University)
Authors: Yang, Chengyu, Li, Zhiming
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2252759615