Measure rigidity of Anosov flows via the factorization method

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.

Expanded version, generalized theorem and various corrections

References in corpus (1)

• Quantitative disjointness of nilflows from horospherical flows

Cited by in corpus (1)

• Open sets of partially hyperbolic skew products having a unique SRB measure