Advanced Dynamical Systems
- Aim:
This is an advanced course in dynamical systems theory.
Participants get acquinted with key results and techniques in modern research topics in dynamics,
with a focus on differentiable dynamics and ergodic theory.
- Description:
Topics will be decided with the partipants. Possible topics are:
- Ergodicity of Anosov diffeomorphisms and the Hopf argument
- Measure theoretic entropy and the variational principle
- Entropy and the Shannon-McMillan-Breiman theorem
- Absolutely continuous invariant measures and the Benedicks-Carleson-Jacobson theorem
- Multiplicative ergodic theorem and nonuniform hyperbolicity
- Homoclinic tangencies and the Newhouse phenomenon
- Organisation:
Seminar
- Examination:
Assignments and presentations by participants
- Literature:
Depending on the chosen topics
- Prerequisites:
Knowledge as contained in a basic master course in dynamical systems or ergodic theory is assumed.
Contents
- February 6: Discussion of topics. First topic to treat is "Newhouse phenomenon", chapters 4,6 and appendix 4 from [PT]:
J. Palis, F. Takens,
Hyperbolicity and sensitive chaotic dynamics at homoclinic bifurcations
1993
- February 13: Ale Jan Homburg: Discussion of contents of chapters 1,2,3, appendix 1,2 in [PT]
- February 20: Thomas van de Leur: [PT] section 4.1, start of section 4.2
- February 27: Christian Hamster: [PT] rest of section 4.2
- March 6: Martino Pitruzzella: [PT] section 4.3
- March 13: Judith Berendsen: [PT] section 6.1,2,3
- March 20: Jan Jelle de Wit [PT] section 6.3,4,5,6
- April 3: Ale Jan Homburg: Discussion of Newhouse phenomenon
- April 10: Start of second topic, Ergodicity of volume preserving Anosov diffeomorphisms from [BT]:
M. Brin, G. Stuck,
Introduction to Dynamical Systems
2003
First lecture: Thomas van de Leur: [BS] section 6.1, start of section 6.2
- April 17: Christian Hamster: [BS] remaining part of section 6.2
- April 30 (at 15:00 in SP G3.05): Judith Berendsen: [BS] section 6.3
-
May 8: Ale Jan Homburg: Fubini foiled
- May 15: Jan Jelle de Wit: Prevalence
-
May 22: Martino Pitruzzella: Nonuniformly hyperbolic diffeomorphisms