Dynamics seminar: Frank Lin (BGU) A topological dynamical system with two different positive sofic entropies

Tue, 04/05/202114:00-15:00
Abstract: Entropy is an important conjugacy invariant in dynamical systems in both the topological and measure-theoretic case.  Sofic entropy, first introduced by L. Bowen in the measure theoretic case and expanded to the topological case by Kerr-Li, is a generalization of classical entropy to dynamical systems acted upon by sofic groups, a very general class of groups of which a non-example is still not known.  A group is sofic if it has a sofic approximation - a sequence of partial actions on finite sets that asymptotically approximates the group acting on itself by left multiplication.  A group may have many sofic approximations, and the definition of sofic entropy a priori depends on the choice of sofic approximation (when the group is nonamenable), but all previously known examples come from degenerate behavior.  Inspired from random hypergraph coloring literature, we provide a nondegenerate example - a mixing action with two sofic approximations giving two different positive topological sofic entropies.  Joint work with Dylan Airey and Lewis Bowen. 

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