Ergodic optimization for Anosov diffeomorphisms

Author(s)

Lino Ramada Ferreira Junior

• Document type: Master's Dissertation
• Press: Campinas, SP.
• Institution: Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica
• Defense date: 2015-02-27

Examining board members

Eduardo Garibaldi; Pedro Jose Catuogno; Ricardo dos Santos Freire Júnior

• Advisor: Eduardo Garibaldi

Abstract

In this master's thesis, we study ergodic optimization techniques in the context of an Anosov dynamical system. We present different approaches to the problem of maximization of the integral of Hölder potentials on a compact metric space in the presence of a hyperbolic dynamics. We discuss the thermodynamical formalism in an expansive model, obtaining maximizing probabilities at zero temperature. In the hyperbolic case, we determine a cohomological inequality in an amphidynamical system, from which follows a Lipschitz subaction for Lipschitz potentials associated with Anosov diffeomorphisms. Finally, we argue that periodic probabilities are maximizing for open sets of functions in the Lipschitz topology (AU)

• FAPESP's process: 12/19977-1 - Ergodic Optimization for Anosov Diffeomorphisms
• Grantee: Lino Ramada Ferreira Junior
• Support Opportunities: Scholarships in Brazil - Master