Translator Disclaimer
2022 First-return maps of Birkhoff sections of the geodesic flow
Théo Marty
Algebr. Geom. Topol. 22(5): 2355-2394 (2022). DOI: 10.2140/agt.2022.22.2355

Abstract

Given a hyperbolic orientable surface and a collection of periodic geodesics on it, we study the Birkhoff sections for the geodesic flow on the unit bundle to the surface bounded by this collection. The first-return maps on these Birkhoff sections are pseudo-Anosov maps, which we explicitly compute. We show that there is a canonical identification of all those Birkhoff sections, and that the first-return maps induced by the flow can all be expressed as a composition of negative Dehn twists along a family of explicit curves; only the order depends on the choice of a particular Birkhoff section.

Citation

Download Citation

Théo Marty. "First-return maps of Birkhoff sections of the geodesic flow." Algebr. Geom. Topol. 22 (5) 2355 - 2394, 2022. https://doi.org/10.2140/agt.2022.22.2355

Information

Received: 29 September 2020; Revised: 10 March 2021; Accepted: 8 May 2021; Published: 2022
First available in Project Euclid: 10 November 2022

Digital Object Identifier: 10.2140/agt.2022.22.2355

Subjects:
Primary: 37D20 , 57M50

Keywords: Birkhoff section , fibered face , first-return map , geodesic flow

Rights: Copyright © 2022 Mathematical Sciences Publishers

JOURNAL ARTICLE
40 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.22 • No. 5 • 2022
MSP
Back to Top