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Persistence of Bowen-Ruelle-Sinai measures

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  • 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.
    Mathematics Subject Classification: 37A35, 37C40, 37D25.


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