The Besicovitch Metric on the Space of G -invariant Ergodic Measures

Abstract: Given two sequences over a finite alphabet, one can measure the distance between them by looking how their asymptotic behaviours differ. This gives rise to dynamically generated Besicovitch pseudometric. I will talk about the generalisation of this concept to actions of countable amenable groups. I will show that it induces a metric on the space of ergodic measures invariant under the action, and that in the case of the shift space, entropy function is continuous with respect to this metric. As an application of these results, I will show that if the considered group is in addition residually finite, then uniquely ergodic measures are entropy dense in the set of totally ergodic measures. This is a joint work with Martha Łącka.

dynamical systems

Audience: researchers in the topic

Dynamical systems seminar at the Jagiellonian University