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Geodesic Flows Modelled by Expansive Flows

Part of: Symplectic geometry, contact geometry Dynamical systems with hyperbolic behavior Measure-theoretic ergodic theory Global differential geometry

Published online by Cambridge University Press:  28 August 2018

Katrin Gelfert  and
Rafael O. Ruggiero
Katrin Gelfert*
Affiliation:
Instituto de Matemática, Universidade Federal do Rio de Janeiro, Cidade Universitária – Ilha do Fundão, Rio de Janeiro 21945-909, Brazil ([email protected])
Rafael O. Ruggiero
Affiliation:
Departamento de Matemática PUC-Rio, Rua Marqués de São Vicente 225, Rio de Janeiro 22543-900, Brazil ([email protected])
*
*Corresponding author.
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Abstract

Given a smooth compact surface without focal points and of higher genus, it is shown that its geodesic flow is semi-conjugate to a continuous expansive flow with a local product structure such that the semi-conjugation preserves time parametrization. It is concluded that the geodesic flow has a unique measure of maximal entropy.

Keywords

expansive flowgeodesic flowconjugate pointsfocal pointstime-preserving semi-conjugacymeasure of maximal entropy

MSC classification

Primary: 53D25: Geodesic flows
Secondary: 53C22: Geodesics 37D40: Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) 37D25: Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) 37D35: Thermodynamic formalism, variational principles, equilibrium states 28D20: Entropy and other invariants 28D99: None of the above, but in this section
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 62 , Issue 1 , February 2019 , pp. 61 - 95
Copyright
Copyright © Edinburgh Mathematical Society 2018 

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