Conservative surface homeomorphisms with finitely many periodic points

DOI10.1007/S11784-022-00936-XarXiv2008.00306MaRDI QIDQ6346299

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Publication date: 1 August 2020

Abstract: The goal of the article is to characterize the conservative homeomorphisms of a closed orientable surface $S$ of genus $geq2$, that have finitely many periodic points. By conservative, we mean a map with no wandering point. As a particular case, when $S$ is furnished with a symplectic form, we characterize the symplectic diffeomorphisms of $S$ with finitely many periodic points.

Mathematics Subject Classification ID

Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25) Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces (37E30) Rotation numbers and vectors (37E45)

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