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Explore fundamental concepts of Smooth Ergodic Theory in this 67-minute lecture focusing on the statistical behavior of dynamical system orbits. Delve into the role of dynamical foliations (stable/unstable) in analyzing statistical properties of hyperbolic systems. Learn about SRB measures and their significance in describing statistical behavior across large point sets. Examine Hopf's argument for proving ergodicity in conservative systems, and understand how SRB measures function as optimal invariant measures for dissipative hyperbolic systems when volume preservation is absent. Master the construction and essential properties of SRB measures while gaining insights into their compatibility with volume in non-volume-preserving scenarios.
