On non-contractible periodic orbits and bounded deviations

Author:

Liu Xiao-ChuanORCID,Tal Fábio ArmandoORCID

Abstract

Abstract We present a dichotomy for surface homeomorphisms in the isotopy class of the identity. We show that, in the absence of a degenerate fixed point set, either there exists a uniform bound on the diameter of orbits of non-wandering points for the lifted dynamics in the universal covering space, or the map has non-contractible periodic orbits. We then use this new tool to characterize the dynamics of area preserving homeomorphisms of the torus without non-contractible periodic orbits, showing that if the fixed point set is non-degenerate, then either the lifted dynamics is uniformly bounded, or it has a single strong irrational dynamical direction.

Funder

Centros de Pesquisa, Inovação e Difusão, Fundação Amazônia Paraense de Amparo à Pesquisa

Publisher

IOP Publishing

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