SRB Measures and Young Towers - Lecture 2 of 4

Explore the second part of a four-part mini-course on Markov Partitions and Young Towers in Dynamics, focusing on SRB Measures and Young Towers. Delve into the groundbreaking techniques developed by Sinai, Ruelle, and Bowen in the 1970s, which revolutionized the application of Ergodic Theory to differentiable dynamical systems. Examine how these methods led to the construction of Markov Partitions and Symbolic Coding for Uniformly Hyperbolic systems, enabling the application of statistical mechanics to describe system properties through SRB measures. Investigate recent advancements in extending these results to Nonuniformly Hyperbolic systems, including those with discontinuities and singularities. Learn about Lai-Sang Young's innovative Young Tower construction and Sarig's generalization of infinite Markov Partitions. Gain insights into the technical challenges and powerful applications of these approaches in studying dynamical systems of great interest. This comprehensive lecture, part of the "Markov Partitions and Young Towers in Dynamics" mini-course convened by José Ferreira Alves, offers an in-depth exploration of these advanced topics in dynamical systems theory.