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Please use this identifier to cite or link to this item: https://hdl.handle.net/20.500.12008/44753 How to cite
Title: Geodesic tracking and the shape of ergodic rotation sets
Authors: García-Sassi, Alejo
Guihéneuf, Pierre-Antoine
Lessa Echeverriarza, Pablo
Type: Preprint
Descriptors: MATHEMATICS - DYNAMICAL SYSTEMS
Issue Date: 2024
Abstract: 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 finite number of pieces that are either one-dimensional or almost convex. The latter ones give birth to horseshoes; in the case of a zero-entropy homeomorphism we show that there exists a geodesic lamination containing the directions in which generic orbits with respect to ergodic invariant probabilities turn around the surface under iterations of the homeomorphism. The proof is based on the idea of geodesic tracking of orbits that are typical for some invariant measure by geodesics on the surface, that allows to get links between the dynamics of such points and the one of the geodesic flow on some invariant subset of the unit tangent bundle of the surface.
Description: Disponible también en: HAL science ouverte, 2024. hal-04491543
Publisher: arXiv
IN: Mathematics (Dynamical Systems), arXiv:2312.06249v2, mar. 2024, pp. 1-84
Citation: García-Sassi, A, Guihéneuf, P y Lessa Echeverriarza, P. "Geodesic tracking and the shape of ergodic rotation sets" [Preprint]. Publicado en: Mathematics (Dynamical Systems). 2024 arXiv:2312.06249v2, mar. 2024, pp. 1-84.
License: Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0)
Appears in Collections:Publicaciones académicas y científicas - Facultad de Ciencias

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