Pressure and conformal measures on generalized countable Markov shifts.

ABSTRACT: From a generalization of the notion of countable Markov shifts developed by R. Exel and M. Laca, which includes the standard shift space, we developed its corresponding thermodynamic formalism and its connections with the standard one. This space includes extra elements that correspond to finite words. A notion of pressure introduced by M. Denker and M. Yuri for Iterated Function Systems (IFS), that considers these finite words as well, is a natural definition for the pressure in this generalized setting. We proved, for a wide class of potentials, that their pressure coincides with the Gurevich pressure. For transitive matrices, even for infinite Gurevich entropy, we found new conformal measures. When the entropy is finite, it plays a crucial role in the critical value of temperature. We highlight an example of a shift space that has uncountable many of these extremal conformal measures.

Posted on May 20, 2021 in Dynamical Systems, Seminars