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arXiv · 2305.05755

Area preserving homeomorphisms of surfaces with rational rotational direction

Pierre-Antoine Guihéneuf·Patrice Le Calvez·Alejandro Passeggi
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Abstract

Let $S$ be a closed surface of genus $g\geq 2$, furnished with a Borel probability measure $λ$ with total support. We show that if $f$ is a $λ$-preserving homeomorphism isotopic to the identity such that the rotation vector $\mathrm{rot}_f(λ)\in H_1(S,\mathbb R)$ is a multiple of an element of $H_1(S,\mathbb Z)$, then $f$ has infinitely many periodic orbits. Moreover, these periodic orbits can be supposed to have their rotation vectors arbitrarily close to the rotation vector of any fixed ergodic Borel probability measure.

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Pierre-Antoine Guihéneuf, Patrice Le Calvez, Alejandro Passeggi. 2023-11-01. Area preserving homeomorphisms of surfaces with rational rotational direction. https://arxiv.org/abs/2305.05755

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