Mini Course - 5 classes

Program: Cohomology Equations: [KH96], [Kat01], [Koc12]. Generalities. "Naive" resolution method. Gotschalk-Hedlund Theorem. Cohomology Obstructions: Invariants measures and distributions. Comology stability. Cohomology (real) of hyperbolic systems: [KH96], [dlLMM86], [Qua97]. Livshitz theorem (Holder regularity) Llave-Marco-Moriyon theorem. Some results about rigidity of hyperbolic systems. Cohomology of elliptic systems and distributional unique ergodic systems: [Kat01], [Hur01], [For08], [Koc09], [AK11], [AFK12]. Cohomology equations for translations in the torus. Katok-Herman conjecture about classification of cohomology rigid systems. "Exotics" examples of DUE systems. Dynamic Cohomology with coefficients in non-commutative groups: [Kat01], [Kal11].