Chaotic Dynamics in Nonautonomous Maps: Application to the Nonautomous Henon Map
Dynamical Systems
2017-05-30 v1
Abstract
In this paper we analyze chaotic dynamics for two dimensional nonautonomous maps through the use of a nonautonomous version of the Conley-Moser conditions given previously. With this approach we are able to give a precise definition of what is meant by a chaotic invariant set for nonautonomous maps. We extend the nonautonomous Conley-Moser conditions by deriving a new sufficient condition for the nonautonomous chaotic invariant set to be hyperbolic. We consider the specific example of a nonautonomous H\'enon map and give sufficient conditions, in terms of the parameters defining the map, for the nonautonomous H\'enon map to have a hyperbolic chaotic invariant set.
Cite
@article{arxiv.1705.10216,
title = {Chaotic Dynamics in Nonautonomous Maps: Application to the Nonautomous Henon Map},
author = {Francisco Balibrea-Iniesta and Carlos Lopesino and Stephen Wiggins and Ana M. Mancho},
journal= {arXiv preprint arXiv:1705.10216},
year = {2017}
}