Continuum-wise expansive homeomorphisms on Peano continua
Dynamical Systems
2007-05-23 v1
Abstract
On a Peano continuum, all local stable and unstable components of a continuum-wise expansive homeomorphism are non trivial. In particular, there is sensitive dependence on initial conditions. This generalizes results in \cite{h,l} about lack of Lyapunov stable points (weak sinks) and existence of non trivial stable and unstable components for expansive homeomorphisms on Peano continua. We also use this fact to generalize a result in \cite{ktt}: a Peano curve admitting a continuum-wise expansive homeomorphism is nowhere rim-countable. However, it is not resolved the question of whether such a dynamics could be possible in a locally planar Peano curve. Some other questions are posed.
Cite
@article{arxiv.math/0406442,
title = {Continuum-wise expansive homeomorphisms on Peano continua},
author = {Jana Rodriguez Hertz},
journal= {arXiv preprint arXiv:math/0406442},
year = {2007}
}