Sensitive dependence of geometric Gibbs measures at positive temperature

ABSTRACT:

In this talk we give the main ideas of the construction of  the first example of a smooth family of real and complex maps having sensitive dependence of geometric Gibbs states at positive temperature. This family consists of quadratic-like maps that are non-uniformly hyperbolic in a strong sense. We show that for a dense set of maps in the family the geometric Gibbs states diverge at positive temperature. These are the first examples of divergence at positive temperature in statistical mechanics or the thermodynamic formalism, and answers a question of van Enter and Ruszel.

Posted on Jul 18, 2018 in Dynamical Systems, Seminars