SRB Measures and Young Towers - Lecture 1

Explore the foundations of Sinai-Ruelle-Bowen (SRB) measures and Young Towers in dynamical systems through this comprehensive mini-course lecture. Delve into the groundbreaking ideas developed by Sinai, Ruelle, and Bowen in the 1970s, which revolutionized the application of Ergodic Theory to differentiable dynamical systems. Learn how Markov Partitions and Symbolic Coding with finite symbols enabled the description of statistical properties in Uniformly Hyperbolic systems. Discover the recent advancements in extending these results to 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 of great interest. This lecture, part of a series convened by José Ferreira Alves from the University of Porto, Portugal, provides an excellent introduction to these complex topics for those with a basic understanding of Uniformly Hyperbolic Dynamics.