Teoria Ergódica Diferenciável - Aula 21

Explore advanced concepts in Differentiable Ergodic Theory through this doctoral-level lecture delivered in Portuguese by Professor Marcelo Viana at IMPA (Instituto de Matemática Pura e Aplicada). Delve into key topics including invariant measures and recurrence, Poincaré and Birkhoff Recurrence Theorems, torus rotations, conservative transformations and flows, and the existence of invariant measures. Master weak* topology, von Neumann and Birkhoff ergodic theorems, and subadditive ergodic theorem. Study ergodicity, Bernoulli shifts, torus linear endomorphisms, ergodic decomposition theorem, measurable partitions, and Rokhlin's disintegration theorem. Examine ergodic uniqueness, minimality, translations in topological groups, Haar measure, correlation decay, mixing systems, Markov shifts, ergodic and spectral equivalence, and Ornstein's theorem. Learn about entropy, Kolmogorov-Sinai theorem, Shannon-McMillan-Breiman theorem, topological entropy, finite type shifts, variational principle, and expanding transformations on manifolds, complemented by additional advanced topics in ergodic theory and dynamical systems.