## Advanced Studies in Pure Mathematics

### Genus one Birkhoff sections for the geodesic flows of hyperbolic 2-orbifolds

#### Abstract

A hyperbolic 2-sphere is made from the double of an $n$-gon in Poincaré disc. Its geodesic flow is a transitive Anosov flow. We construct genus one Birkhoff sections for the geodesic flows of hyperbolic 2-spheres with $n$ ($\ge 3$) singularities.

#### Article information

Dates
Revised: 1 December 2014
First available in Project Euclid: 4 October 2018

https://projecteuclid.org/ euclid.aspm/1538671776

Digital Object Identifier
doi:10.2969/aspm/07210367

Mathematical Reviews number (MathSciNet)
MR3726719

Zentralblatt MATH identifier
1393.37044

#### Citation

Hashiguchi, Norikazu; Minakawa, Hiroyuki. Genus one Birkhoff sections for the geodesic flows of hyperbolic 2-orbifolds. Geometry, Dynamics, and Foliations 2013: In honor of Steven Hurder and Takashi Tsuboi on the occasion of their 60th birthdays, 367--386, Mathematical Society of Japan, Tokyo, Japan, 2017. doi:10.2969/aspm/07210367. https://projecteuclid.org/euclid.aspm/1538671776