Instytut Matematyczny Polskiej Akademii Nauk / Institute of Mathematics / Publishing house / Journals and Serials / Fundamenta Mathematicae / All issues

Abstract

We study the multifractal formalism for Lyapunov exponents of typical one-step 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 for Lyapunov exponents holds for typical one-step cocycles. Furthermore, we prove a variational principle for the generalized singular value function.