Regularity of foliations and Lyapunov exponents of partially hyperbolic dynamics

TL;DR

This paper explores how the smoothness of invariant foliations relates to Lyapunov exponents in partially hyperbolic systems, proposing a new regularity condition as a criterion for Lyapunov exponent rigidity.

Contribution

It introduces a novel regularity condition for foliations based on Lebesgue measure disintegration, linking foliation regularity to Lyapunov exponent rigidity.

Findings

Proposes a new regularity criterion for foliations.

Establishes a connection between foliation regularity and Lyapunov exponents.

Suggests conditions for rigidity of Lyapunov exponents.

Abstract

In this work we study relations between regularity of invariant foliations and Lyapunov exponents of partially hyperbolic diffeomorphisms. We suggest a new regularity condition for foliations in terms of desintegration of Lebesgue measure which can be considered as a criterium for rigidity of Lyapunov exponents.