Abstract:
In this talk, we will explore the multifractal analysis of the Lyapunov exponent function, also known as the Lyapunov spectrum. About 25 years ago, Weiss and Pesin applied thermodynamic formalism to study the Lyapunov spectrum for Anosov diffeomorphisms. Their results have since been generalized to various settings, including non-uniformly hyperbolic systems and non-compact spaces. We will begin with a brief introduction to thermodynamic formalism, followed by a discussion of this problem in the context of certain dynamical systems on the interval that exhibit intriguing phenomena related to the topological pressure function.