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April  2007, 17(2): 403-422. doi: 10.3934/dcds.2007.17.403

Cohomology and subcohomology problems for expansive, non Anosov geodesic flows

Artur O. Lopes 1, , Vladimir A. Rosas 2, and  Rafael O. Ruggiero 3,

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, Brazil
2. 

Departamento Académico de Matemática y Estadística, Universidad Nacional de San Agustín, Calle Santa Catalina 117, Arequipa, Perú, Peru
3. 

Departamento de Matemática, Pontificia Universidade Católica do Rio de Janeiro, Rua Marqués de São Vicente 225, Gávea, Rio de Janeiro, Brazil

Received  December 2005 Revised  September 2006 Published  November 2006

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.
Keywords: action functions, Livsic Theorem, subaction functions, Expansive geodesic flow, cohomology of dynamical systems..
Mathematics Subject Classification: 53D25, 37C50, 37C1.
Citation: Artur O. Lopes, Vladimir A. Rosas, Rafael O. Ruggiero. Cohomology and subcohomology problems for expansive, non Anosov geodesic flows. Discrete and Continuous Dynamical Systems, 2007, 17 (2) : 403-422. doi: 10.3934/dcds.2007.17.403
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