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Dynamical Systems Seminar

Finiteness of matrix equilibrium states

  • 演讲者:Jairo Bochi(智利天主教大学)

  • 时间:2020-08-31 20:30-21:30

  • 地点:Zoom (ID 651 5107 9463)

Abstract

I will give a short introduction to subadditive thermodynamical formalism, including the (generalized) singular value pressure and applications to dimensions of non-conformal fractals. Then I will focus on equilibrium states. Sufficient conditions for the equilibrium state to be unique (and to have nice ergodic properties) are known, and these conditions are satisfied generically. What about non-generic situations? In the setting of locally constant cocycles of invertible matrices over a full shift, together with Ian Morris, we prove that the number of ergodic equilibrium states of the singular value pressure is always finite, and we provide a bound; furthermore, we show that all these equilibrium states are fully supported. The proof relies on some tools from algebraic geometry. Finally, I will speculate on extensions of our constructions to more general classes of linear cocycles.


About the speaker

Jairo Bochi is an Associate Professor at the Department of Mathematics at Catholic University of Chile since 2014. Before coming to Santiago de Chile, he has worked as assistant and then associate professor at two major universities in Brazil. He graduated at IMPA (Rio de Janeiro, Brazil) in 2001.

Bochi’s research field is dynamical systems. He has published around 40 papers and has collaborated with more than 30 people from all around the world. He was a speaker at the dynamical systems and differential equations session of the last International Congress of Mathematicians (Rio de Janeiro, 2018).