BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Thiago Raszeja (University of São Paulo (USP)\, Brazil) DTSTART:20210428T131500Z DTEND:20210428T144500Z DTSTAMP:20260423T021858Z UID:DSSUJ/26 DESCRIPTION:Title: T hermodynamic formalism on generalized countable Markov shifts\nby Thia go Raszeja (University of São Paulo (USP)\, Brazil) as part of Dynamical systems seminar at the Jagiellonian University\n\nLecture held in 1016.\n\ nAbstract\nGiven a 0-1 infinite matrix $A$\, R. Exel and M. Laca have\nint roduced a kind of \\textit{generalized countable Markov shift}\n(GCMS) $X_ A=\\Sigma_A \\cup Y_A$\, which is a locally compact (in many\nimportant ca ses compact) version of $\\Sigma_A$\, the standard countable\nMarkov shift . The elements of $Y_A$ are finite words\, possibly\nincluding multiplicit ies. We develop the thermodynamic formalism for\nGCMS\, where we introduce d the notion of conformal measure on $X_A$\,\nand we explored its connecti ons with the usual formalism on\n$\\Sigma_A$. Among the results\, we highl ight the finding of new\nconformal measures that are not detected by the t hermodynamic\nformalism on $\\Sigma_A$ and new phase transition phenomena: for a wide\nclass of GCMS and potentials\, we determined regions for the inverse of\nthe temperature $\\beta$\, where we absence\\existence of thes e new\nconformal probabilities\, living on $Y_A$. The Gurevich entropy $h_ G$\nplays a fundamental role in determining these regions since the\ncriti cal value for gauge potentials is $h_G$ when finite. We also have\nphase t ransition results for $h_G = \\infty$\, including the full shift.\nIn addi tion\, for the eigenmeasures of Ruelle's transformation\, we\ndiscovered a length-type phase transition in the renewal shift: the\nexistence of a cr itical value for $\\beta$ where the measure passes\nfrom living on $\\Sigm a_A$ to live on $Y_A$. We showed that the notion\nof pressure introduced b y M. Denker and M. Yuri for Iterated Function\nSystems (IFS) is a natural definition of pressure for $X_A$\, and it\ncoincides with the Gurevich pre ssure for GCMS basically for the same\ngenerality on which the thermodynam ic formalism is developed for the\nstandard countable Markov shifts and po tentials.\n\nJoint work with R. Bissacot (University of São Paulo (USP)\, Brazil)\,\nR. Exel (Federal University of Santa Catarina (UFSC)\, Brazil) \, and R.\nFrausino (University of Wollongong (UOW)\, Australia).\n LOCATION:https://researchseminars.org/talk/DSSUJ/26/ END:VEVENT END:VCALENDAR