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January  2001, 7(1): 177-202. doi: 10.3934/dcds.2001.7.177

SRB measures of certain almost hyperbolic diffeomorphisms with a tangency

Eleonora Catsigeras 1, and  Heber Enrich 1,

1. 

Instituto de Matemática, Universidad de la República, Uruguay, Uruguay

Received  December 1999 Revised  October 2000 Published  November 2000

We study topological and ergodic properties of some almost hyperbolic diffeomorphisms on two dimensional manifolds. Under generic conditions, diffeomorphisms obtained from Anosov by an isotopy pushing together the stable and unstable manifolds to be tangent at a fixed point, are conjugate to Anosov. For a finite codimension subset at the boundary of Anosov there exist a SRB measure and an unique ergodic attractor.
Keywords: Lyapounov functions, expansive maps., boundary of Anosov, SBR measures, almost hyperbolic systems, distortion bounds, nonuniformly hyperbolic systems, almost Anosov, Measure preservation, conjugation to Anosov, ergodic attractors.
Mathematics Subject Classification: 28D05, 37A05, 37B25, 37C40, 37D2.
Citation: Eleonora Catsigeras, Heber Enrich. SRB measures of certain almost hyperbolic diffeomorphisms with a tangency. Discrete & Continuous Dynamical Systems, 2001, 7 (1) : 177-202. doi: 10.3934/dcds.2001.7.177
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