Expansive homeomorphisms of the plane

Details Expansive homeomorphisms of the plane Expansive homeomorphisms of the plane

2009-06-25

arxiv.org/abs/0906.4596v1

Discrete and Continuous Dynamical Systems, 29(2011), no 1, 213--239

Mathematics

Dynamical Systems

29 pages, 22 figures

Scientific paper

10.3934/dcds.2011.29.213

This article tackles the problem of the classification of expansive homeomorphisms of the plane. Necessary and sufficient conditions for a homeomorphism to be conjugate to a linear hyperbolic automorphism will be presented. The techniques involve topological and metric aspects of the plane. The use of a Lyapunov metric function which defines the same topology as the one induced by the usual metric but that, in general, is not equivalent to it is an example of such techniques. The discovery of a hypothesis about the behavior of Lyapunov functions at infinity allows us to generalize some results that are valid in the compact context. Additional local properties allow us to obtain another classification theorem.

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