Advanced Studies in Pure Mathematics

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

Norikazu Hashiguchi and Hiroyuki Minakawa

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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

Source
Geometry, Dynamics, and Foliations 2013: In honor of Steven Hurder and Takashi Tsuboi on the occasion of their 60th birthdays, T. Asuke, S. Matsumoto and Y. Mitsumatsu, eds. (Tokyo: Mathematical Society of Japan, 2017), 367-386

Dates
Received: 30 June 2014
Revised: 1 December 2014
First available in Project Euclid: 4 October 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1538671776

Digital Object Identifier
doi:10.2969/aspm/07210367

Mathematical Reviews number (MathSciNet)
MR3726719

Zentralblatt MATH identifier
1393.37044

Subjects
Primary: 37D40: Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
Secondary: 57R18: Topology and geometry of orbifolds 57R30: Foliations; geometric theory

Keywords
Birkhoff section hyperbolic orbifold geodesic flow transitive Anosov flow

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


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