Measure rigidity of Anosov flows via the factorization method

DOI10.1007/S00039-023-00629-8arXiv1910.14091MaRDI QIDQ6328215

Publication date: 30 October 2019

Abstract: Using the factorization method, a method pioneered by Eskin and Mirzakhani in their groundbreaking work about measure classification over the moduli space of translation surfaces, we show that generalized

u

-Gibbs states over quantitatively non-integrable Anosov systems are absolutely continuous with respect to the whole unstable manifold.

Mathematics Subject Classification ID

Geometric group theory (20F65) Smooth ergodic theory, invariant measures for smooth dynamical systems (37C40) Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Thermodynamic formalism, variational principles, equilibrium states for dynamical systems (37D35) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40)

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