Continuum-wise expansive homeomorphisms on Peano continua

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dc.creatorHertz, Jana Rodriguez
dc.date2004-06-22
dc.date.accessioned2026-07-07T05:09:29Z
dc.date.available2026-07-07T05:09:29Z
dc.descriptionOn 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 $X$ 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.
dc.identifierhttps://arxiv.org/abs/math/0406442
dc.identifierhttp://arxiv.org/abs/math/0406442
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/71643
dc.subjectDynamical Systems
dc.subject54H20; 54F50
dc.titleContinuum-wise expansive homeomorphisms on Peano continua
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