Professor: Alejandro Kocsard

Dates: September 16 - 27, 2013

Program:

Cohomology Equations: [KH96], [Kat01], [Koc12].

- Generalities. "Naive" resolution method.
- Gotschalk-Hedlund Theorem.
- Cohomology Obstructions: Invariants measures and distributions.
- Comology stability.

- Livshitz theorem (Holder regularity)
- Llave-Marco-Moriyon theorem.
- Some results about rigidity of hyperbolic systems.

- Cohomology equations for translations in the torus.
- Katok-Herman conjecture about classification of cohomology rigid systems.
- "Exotics" examples of DUE systems.

References:

[AFK12] Artur Avila, Bassam Fayad, and Alejandro Kocsard, Distributionally

uniquely ergodic diffeomorphisms, Preprint, 2012.

[AK11] Artur Avila and Alejandro Kocsard, Cohomological equations and

invariant distributions for minimal circle diffeomorphisms, Duke Math. J. 158 (2011), no. 3, 501-536. MR 2805066

[dlLMM86] R. de la Llave, J. M. Marco, and R. Moriyón, Canonical perturbation theory of anosov systems and regularity results for the livsic cohomology equation, Annals of Mathematics 123 (1986), no. 3,

537-611. MR MR840722 (88h:58091)