Introduction to Dynamical Cohomology
Professor: Alejandro Kocsard
Dates: September 16 - 27, 2013
Cohomology Equations: [KH96], [Kat01], [Koc12].
Cohomology (real) of hyperbolic systems: [KH96], [dlLMM86],
- Generalities. "Naive"
- Gotschalk-Hedlund Theorem.
- Cohomology Obstructions:
Invariants measures and distributions.
- Comology stability.
Cohomology of elliptic systems and distributional unique ergodic
systems: [Kat01], [Hur01], [For08], [Koc09], [AK11], [AFK12].
- Livshitz theorem (Holder
- Llave-Marco-Moriyon theorem.
- Some results about rigidity
of hyperbolic systems.
Dynamic Cohomology with coefficients in non-commutative
- Cohomology equations for
translations in the torus.
- Katok-Herman conjecture
about classification of cohomology rigid systems.
- "Exotics" examples of DUE
[AFK12] Artur Avila, Bassam Fayad, and Alejandro Kocsard,
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,
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)