31,615

Mini-Curso: Introduction to Dynamical Cohomology

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.
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].

References:

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