Restricted variational principle of Lyapunov exponents for typical cocycles

TL;DR

This paper establishes a variational principle linking topological pressure and measure-theoretic entropy for Lyapunov exponents in typical cocycles, advancing the understanding of their multifractal structure.

Contribution

It introduces a restricted variational principle for Lyapunov exponents in typical cocycles, connecting pressure and entropy through a new formalism.

Findings

Proves the restricted variational principle for typical cocycles.

Links Legendre transform of pressure to measure-theoretic entropy.

Enhances understanding of multifractal formalism for Lyapunov exponents.

Abstract

In this paper, we study the multifractal formalism of Lyapunov exponents for typical cocycles. We establish a variational relation between the Legendre transform of topological pressure of the generalized singular value function and measure-theoretic entropies. As a consequence, we show that the restricted variational principle of Lyapunov exponents holds for typical cocycles.