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Topologically Anosov plane homeomorphisms by Cousillas, Gonzalo; Groisman, Jorge; Xavier, Juliana is a scholarly article available to read on EtoBox.

What is Topologically Anosov plane homeomorphisms about?

This paper deals with classifying the dynamics of {\it Topologically Anosov} plane homeomorphisms. We prove that a Topologically Anosov homeomorphism $f:\mathbb{R}^2 \to \mathbb{R}^2$ is conjugate to a homothety if it is the time one map of a flow. We also obtain results for the cases when the nonwandering set of $f$ reduces to a fixed point, or if there exists an open, connected, simply connected proper subset $U$ such that $U \subset \mathrm{Int}(\overline {f(U)})$, and such that $ \cup_{n\geq 0} f^n (U)= \mathbb{R}^2$. In the general case, we prove a structure theorem for the $\alpha$-limits of orbits with empty $\omega$-limit (or the $\omega$-limits of orbits with empty $\alpha$-limit), and we show that any basin of attraction (or repulsion) must be unbounded.

Author

Cousillas, Gonzalo; Groisman, Jorge; Xavier, Juliana

Published

2018

Language

EN