Livšic Measurable Rigidity Theorem for \mathcal{C}^1 Generic Volume-preserving Systems

Abstract

In this paper, we prove that for ${\mathcal{C}}^1$ generic volume-preserving Anosov diffeomorphisms of a compact Riemannian manifold, Livšic measurable rigidity theorem holds. We also prove that for ${\mathcal{C}}^1$ generic volume-preserving Anosov flows of a compact Riemannian manifold, Livšic measurable rigidity theorem holds.

9 Pages