Title：The joint maximal drift of Euclidean isometries
Speaker：Prof. Jairo Bochi (Penn State University)
Time：19:00, July 3rd, Friday
Venue：5207, the 5th Teaching Building & ZOOM：838 2227 5987
Abstract：Given a finite collection of isometries of a non-compact metric space, we want to compose them in such a way that trajectories tend to infinity as fast as possible. We would like to compute this maximal drift and describe the shift-invariant measures that attain it. This is naturally a problem in Ergodic Optimization. If the ambient space is the hyperbolic plane, the maximal drift is directly related to a joint spectral radius, and it's widely believed that the corresponding maximizing measures are typically supported on periodic orbits. In this talk, we will focus on isometries of the Euclidean plane. In this case, periodic optimizers are no longer typical. Nevertheless, we are able to describe drift-maximizing measures explicitly for a subset of the parameter space with positive Lebesgue measure. A key step in our analysis is a reduction to a problem of standard ergodic optimization over a partially hyperbolic skew-product system. Joint work with Pablo Lessa (Udelar, Uruguay).
About the Speaker：Prof. Jairo Bochi is a Professor of Mathematics at Penn State University. His research focuses on dynamical systems and their connections with geometry, linear algebra, and control theory. He received his Ph.D. from IMPA, Brazil, in 2001. Before joining Penn State in 2021, he held positions at UFRGS, PUC-Rio, and PUC-Chile. He is a member of the Anatole Katok Center for Dynamical Systems and Geometry. He was an invited speaker at the International Congress of Mathematicians in 2018.