On the sensitivities dependence in nonautonomous dynamical systems
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 nonautonomous 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.
 Publication:

arXiv eprints
 Pub Date:
 January 2016
 arXiv:
 arXiv:1602.00075
 Bibcode:
 2016arXiv160200075Y
 Keywords:

 Mathematics  Dynamical Systems;
 37B55
 EPrint:
 13pages