Symbolic Dynamics for Nonuniformly Hyperbolic Systems - Lecture 1 of 5

Delve into the world of symbolic dynamics for nonuniformly hyperbolic systems in this comprehensive mini-course lecture. Explore the groundbreaking ideas and techniques developed by Sinai, Ruelle, and Bowen in the 1970s, which revolutionized the application of Ergodic Theory to differentiable dynamical systems. Learn about Markov Partitions, Symbolic Coding, and the construction of Sinai-Ruelle-Bowen (SRB) measures. Discover the recent advancements in extending these concepts to more general Nonuniformly Hyperbolic systems, including those with discontinuities and singularities. Examine the two main approaches that have emerged: Young Towers and infinite Markov Partitions. Gain insights into the construction of SRB measures and their statistical properties in various dynamical systems. This lecture, part of a series convened by Yuri Lima, provides an excellent foundation for understanding the complexities and challenges of studying nonuniformly hyperbolic systems.