6 papers
Surface homeomorphisms with big rotation set
Pierre-Antoine Guihéneuf
This article consists in applications of [arXiv:2511.14232] in the case of homemomorphisms of higher genus surfaces whose homological rotation set is big enough -- a class of dynam…
A rotational hyperbolic theory for surface homeomorphisms
Pierre-Antoine Guihéneuf
We develop a rotational hyperbolic theory for surface homeomorphisms. We use the equivalence relation on ergodic measures that have nontrivial rotational behaviour defined in [arXi…
Bounded deviations in higher genus II: minimal laminations
Pierre-Antoine Guihéneuf, Fábio Armando Tal
This article follows and completes [arXiv:2511.14222], where we study the problem of bounded deviations for homeomorphisms of closed surfaces of genus . This second part dea…
Bounded deviations in higher genus I: closed geodesics
Pierre-Antoine Guihéneuf, Fábio Armando Tal
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 . This first part studies bounde…
Hyperbolic isometries of the fine curve graph of higher genus surfaces
Pierre-Antoine Guihéneuf, Emmanuel Militon
We prove that for a homeomorphism f that is isotopic to the identity on a closed hyperbolic surface, the following are equivalent: * f acts hyperbolically on the fine curve graph;…
Geodesic tracking and the shape of ergodic rotation sets
Alejo García-Sassi, Pierre-Antoine Guihéneuf, Pablo Lessa
We prove a structure theorem for ergodic homological rotation sets of homeomorphisms isotopic to the identity on a closed orientable hyperbolic surface: this set is made of a finit…