Entropy, f-bar, and Abramov's formula for the entropy of induced transformations

Abstract: Recall that an infinite sequence over a finite alphabet A is quasi-regular, if it is a generic point for a (non-necessarily ergodic) shift-invariant measure. Given a quasi-regular point x in the full shift over A we write h(x) for the Kolmogorov-Sinai entropy of the shift invariant Borel probability measure generated by x. We prove that h is uniformly continuous on the set of all quasi-regular points endowed with the f-bar (pseudo)distance. We also give an alternative proof of Abramov's formula for the entropy of induced transformations. This is a joint work with Tomasz Downarowicz and Martha Łącka.

dynamical systems

Audience: researchers in the topic

Dynamical systems seminar at the Jagiellonian University