May 24, 2021 / 4:30 PM – 5:30 PM (Santiago Time, GMT-4)

     Zoom meeting (ID 948 5787 9126, password required; ask for it at sistemasdinamicoscl@gmail.com)

    Thiago Raszeja (University of São Paulo / AGH University of Science and Technology, Poland)

    Pressure and conformal measures on generalized countable Markov shifts

    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.

    Joint work with R. Bissacot (University of São Paulo (USP), Brazil), R. Exel (Federal University of Santa Catarina (UFSC), Brazil), and R. Frausino (University of Wollongong (UOW), Australia).