Liv\v{s}ic Measurable Rigidity Theorem for \mathcal{C}^1 Generic Volume-preserving Systems

TL;DR

This paper proves that Livšic measurable rigidity holds for generic volume-preserving Anosov diffeomorphisms and flows in the  class on compact manifolds, extending the understanding of rigidity phenomena in dynamical systems.

Contribution

It establishes the Liv
61ic measurable rigidity theorem for  generic volume-preserving Anosov systems, both diffeomorphisms and flows, on compact Riemannian manifolds.

Findings

Liv
61ic measurable rigidity holds for  generic volume-preserving Anosov diffeomorphisms.

Liv
61ic measurable rigidity holds for  generic volume-preserving Anosov flows.

The results extend rigidity phenomena to a broad class of dynamical systems.

Abstract

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