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Recent contributions to the ergodic optimization of maps and flows

Abstract

Ergodic optimization as a branch of ergodic theory aims to describe the set of invariant measures which maximize (or minimize) averages of certain real valued observables. Inspired by applications to Lyapunov exponents and rotation vectors, there are also many recent results addressing both the ergodic optimization of non-additive sequences of observables and of vector valued observables. In this talk I will review some recent results on the ergodic optimization of maps and flows, with particular emphasis on the ergodic optimization of hyperbolic flows and Lorenz attractors.

About the speaker

Paulo Varandas completed his undergraduate studies in Mathematics at University of Porto in 2002, having received the prize for Best Classification in Sciences by the Foundation Eng. António de Almeida. In 2007, he completed the graduate studies at IMPA-Brazil, under supervision of Professor Marcelo Viana. In 2008 he was approved for a permanent position at Federal University of Bahia, in Salvador - Brazil, where he has been a professor ever since. Currently he is on a leave from UFBA and holds a three-year researcher position at University of Porto promoted by the Portuguese Science Foundation - FCT, and conducts research in dynamical systems and ergodic theory. Some of his interests include thermodynamic formalism, decay of correlations, large deviations, non-uniform hyperbolicity, centralizers and topological methods in ergodic theory. He was the head of the PhD Program in Mathematics UFBA-UFAL, has organized some international conferences - among these an ICM Satellite Meeting at UFBA in 2018, was the advisor of several masters and PhD students, and supervisioned post-doctoral fellows.