Eventos Especiais do Grupo de Sistemas Dinâmicos (IM-UFRJ) Limit theorems in dynamical systems using transfer operator methods, Mini-course by Douglas Coates Course notes 27/2-2/3/2023 Hyperbolic groups and Martin boundaries, Mini-course by Manuel Stadlbauer Construction principle of the so called Martin boundary, give examples and first applications ([W], [S], [BS]) | Hyperbolic groups and Ancona's inequality: basic properties of Gromov hyperbolic spaces and discuss, how these geometric features affect the potential theoretic Martin boundary ([A], [BS]) | Analytic tools and a local limit theorem ([KM], [GL], [G], [BS]) References: [A] Ancona, Negatively curved manifolds, elliptic operators, and the Martin boundary. 1987. [BS] Bispo, Stadlbauer, The Martin boundary of an extension by a hyperbolic group. To appear in Israel Journal of Mathematics. arXiv 2005.03723 [G] Gouezel, Local limit theorem for symmetric random walks in Gromov-hyperbolic groups. 2014. [GL] Gouezel, Lalley, Random walks on co-compact Fuchsian groups. 2013. [KM] Karlsson, Margulis, A multiplicative ergodic theorem and nonpositively curved spaces. 1999. [W] Woess, Denumerable Markov chains - EMS Textbooks in Mathematics. 2009. [S] Schwartz, Thermodynamic Formalism for Transient Potential Functions. 2019. Seminários de tópicos satélites 27/2 as 9h00: Operador de Ruelle: Gabriel L. & Juan M. slides 28/2 as 9h00: Espaços métricas hiperholicos au gromov: Eric B., Fabián L. slides 1/3 as 9h00: O bordo de um espaço hiperbolico: Manuel S., Matheus del Valle 1/3 as 11h30: Teorema de Karlsson-Margulis: Heric C. & Lamartine M. slides, notas 2/3 as 9h00: A fronteira de martin: Manuel S.