Work

Deforming a Finsler metric on the two-torus to a flat Finsler metric with conjugate geodesic flows

Year: 2024

Type: article

Abstract: We show that the space of (reversible) Finsler metrics on the two-torus 𝕋 2 whose geodesic flow is conjugate to the geodesic flow of a flat Finsler metric strongly deformation retracts to the space of flat Finsler metrics with respect to the uniform convergence topology. Along the proof, we also show that two Finsler metrics on 𝕋 2 without conjugate points, whose Heber foliations are smooth and with the same marked length spectrum, have conjugate geodesic flows.

Source: Annales Henri Lebesgue

DOI: 10.5802/ahl.217

Authors: Elie Nakhlé, Stéphane Sabourau

Institutions: Centre National de la Recherche Scientifique, Université Paris-Est Créteil, Laboratoire d’Analyse et de Mathématiques Appliquées, Université Gustave Eiffel

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: Agence Nationale de la Recherche

Awards: G3010527862, Min-max constructions in geometry and topology