2004/06/22 by Jana Rodriguez Hertz, Hertz, Jana Rodriguez
Mathematics · #54F50 #54H20 #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Mathematical Dynamics and Fractals #math.DS #msc:54F50 #msc:54H20
paper · pdf · doi:10.48550/arxiv.math/0406442
arxiv created 2004/06/22 · openalex publication_date 2004/06/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 \citeh,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 \citektt: 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.