Flexibility of Lyapunov exponents

TL;DR

This paper explores the adaptability of Lyapunov exponents in smooth dynamical systems, particularly for volume-preserving diffeomorphisms with certain structural properties, demonstrating their potential for varied dynamical behaviors.

Contribution

It establishes new flexibility results for Lyapunov exponents in Anosov diffeomorphisms with dominated splittings into one-dimensional bundles.

Findings

Lyapunov exponents can be varied within certain classes of diffeomorphisms.

Flexibility results apply to volume-preserving Anosov systems with one-dimensional splittings.

The work advances understanding of the possible Lyapunov spectrum configurations.

Abstract

We outline the flexibility program in smooth dynamics, focusing on flexibility of Lyapunov exponents for volume-preserving diffeomorphisms. We prove flexibility results for Anosov diffeomorphisms admitting dominated splittings into one-dimensional bundles.