Stably non-synchronizable maps of the plane
Dynamical Systems
2016-09-07 v1
Abstract
Pecora and Carroll presented a notion of synchronization where an (n-1)-dimensional nonautonomous system is constructed from a given -dimensional dynamical system by imposing the evolution of one coordinate. They noticed that the resulting dynamics may be contracting even if the original dynamics are not. It is easy to construct flows or maps such that no coordinate has synchronizing properties, but this cannot be done in an open set of linear maps or flows in , . In this paper we give examples of real analytic homeomorphisms of such that the non-synchronizability is stable in the sense that in a full neighborhood of the given map, no homeomorphism is synchronizable.
Cite
@article{arxiv.math/9702225,
title = {Stably non-synchronizable maps of the plane},
author = {Patrice Le Calvez and Marco Martens and Charles Tresser and Patrick A. Worfolk},
journal= {arXiv preprint arXiv:math/9702225},
year = {2016}
}