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arXiv · 2511.14222

Bounded deviations in higher genus I: closed geodesics

Pierre-Antoine Guihéneuf·Fábio Armando Tal
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Abstract

This is the first article of a series of two where we study the problem of bounded deviations for homeomorphisms of closed surfaces of genus $\ge 2$. This first part studies bounded deviations with respect to closed geodesics. As a byproduct of our proofs, we also get a criterion of existence of periodic orbits in terms of big deviation with respect to some closed geodesic. The combination with the second part [arXiv:2511.14226] generalises to the higher genus case most of the bounded deviations results already known for the torus.

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Pierre-Antoine Guihéneuf, Fábio Armando Tal. 2025-11-18. Bounded deviations in higher genus I: closed geodesics. https://arxiv.org/abs/2511.14222

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