Mini-Curso: Introduction to Dynamical Cohomology

Professor: Alejandro Kocsard
Dates:  September 16 - 27, 2013

Program:

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

Dynamic Cohomology with coefficients in non-commutative groups: [Kat01], [Kal11].

References:

[AFK12] Artur Avila, Bassam Fayad, and Alejandro Kocsard, Distributionally
uniquely ergodic diffeomorphisms, Preprint, 2012.
[AK11] Artur Avila and Alejandro Kocsard, Cohomological equations and

 

DOWNLOAD

Aula 01 - 18.07.2013 - download
Aula 02 - 20.07.2013 - download
Aula 03 - 23.07.2013 - download
Aula 04 - 25.07.2013 - download
Aula 05 - 27.07.2013 - download

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