Entropy spectrum of Lyapunov exponents for typical cocycles

TL;DR

This paper investigates the structure of Lyapunov exponents' level sets in typical cocycles, revealing a variational principle linking their topological entropy to topological pressure.

Contribution

It establishes a novel variational relation between entropy and pressure for Lyapunov exponent level sets in typical cocycles.

Findings

Derived a variational formula connecting entropy and pressure.

Characterized the size of Lyapunov exponent level sets.

Extended understanding of dynamical complexity in cocycles.

Abstract

In this paper, we study the size of the level sets of all Lyapunov exponents. For typical cocycles, we establish a variational relation between the topological entropy of the level sets of Lyapunov exponents and the topological pressure of the generalized singular value function.