Cohomology and subcohomology problems for expansive, non Anosov geodesic flows

Artur O. Lopes; Vladimir A. Rosas; Rafael O. Ruggiero

doi:10.3934/dcds.2007.17.403

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2007, Volume 17, Issue 2: 403-422. Doi: 10.3934/dcds.2007.17.403

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Cohomology and subcohomology problems for expansive, non Anosov geodesic flows

1.
Instituto de Matemática, Dep. de Matemática Pura e Aplicada, Universidade Federal do Rio Grande do Sul, Av. Bento Gon¸calves 9500, Porto Alegre, 91500
2.
Departamento Académico de Matemática y Estadística, Universidad Nacional de San Agustín, Calle Santa Catalina 117, Arequipa, Perú
3.
Departamento de Matemática, Pontificia Universidade Católica do Rio de Janeiro, Rua Marqués de São Vicente 225, Gávea, Rio de Janeiro

Received: November 30, 2005

Revised: August 31, 2006

Published: April 2007

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Abstract

We show that there are examples of expansive, non-Anosov geodesic flows of compact surfaces with non-positive curvature, where the Livsic Theorem holds in its classical (continuous, Hölder) version. We also show that such flows have continuous subaction functions associated to Hölder continuous observables.

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Mathematics Subject Classification: 53D25, 37C50, 37C15.

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