# American Institute of Mathematical Sciences

2007, 17(1): 213-221. doi: 10.3934/dcds.2007.17.213

## Persistence of Bowen-Ruelle-Sinai measures

 1 Centro de Matemática da Universidade do Porto, Faculdade de Ciências, Rua do Campo Alegre, 687, 4169-007 Porto, Portugal

Received  January 2005 Revised  August 2006 Published  October 2006

We study the changes on the Bowen-Ruelle-Sinai measures along an arc that starts at an Anosov diffeomorphism on a two-torus and reaches the boundary of its stability component while a flat homoclinic tangency or a first cubic heteroclinic tangency is happening. The outermost diffeomorphisms of such arcs are not hyperbolic but are conjugate to the original Anosov diffeomorphism and share similar ergodic traits. In particular, the torus is a global attractor with a full supported physical measure.
Citation: Maria Pires De Carvalho. Persistence of Bowen-Ruelle-Sinai measures. Discrete & Continuous Dynamical Systems - A, 2007, 17 (1) : 213-221. doi: 10.3934/dcds.2007.17.213
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