Flexibility and rigidity for Cantor repellers

Abstract: We will consider dynamical systems that we call Cantor repellers which are expanding maps on invariant Cantor sets coming from iterated function systems. Cantor repellers have two natural invariant measures: the measure of full dimension and the measure of maximal entropy. We show that dimensions and Lyapunov exponents of those measures are flexible up to well understood restrictions. We will also discuss the boundary case for the range of values of the considered dynamical data. This is joint work with Jacob Mazor.

dynamical systemsnumber theory

Audience: general audience

New England Dynamics and Number Theory Seminar