Prof. D. Kotschick and Prof. T. Vogel: Seminar on the Geometry of Anosov systems

The following talks are based on the references listed at the end. The papers by Anosov [A] and Smale [S] are good general references for a lot of the early talks.

Further talks may be added according to the interests of the participants.



 
18 April D. Kotschick  Introduction, basic definitions and examples
25 April L. Garcia  Stable and unstable foliations, openness/genericity 
[AA] par 15 + Appendix 22
2 May F. Semrau  Structural stability of:
overtwisted disks [HS] 16.3; Anosov systems [KH] 2.3, [AA] par 16 + Appendix 25, [S]
9 May A. Strzelczyk  Density of un-/stable manifolds
[P1] 1.
23 May T. Vogel Anosov closing lemma; geodesic flows
30 May N. Pia  Anosov flows with invariant transverse foliations
[P1] 2.+3.
6 June M. Scandi  Anosov flows with invariant forms; closed orbits
[P1] 4. + [P2]
27 June F. Semrau Anosov flows and the fundamental group
[PT]

References:
[A] D. V. Anosov: Geodesic flows on closed Riemann manifolds with negative curvature. Proceedings of the Steklov Institute of Mathematics, No. 90 (1967). American Mathematical Society Translations, Providence, R.I. 1969.
[AA] V. I. Arnold and A. Avez: Ergodic problems of classical mechanics. W. A. Benjamin, Inc., New York-Amsterdam 1968.
[HS] M. W. Hirsch and S. Smale: Differential equations, dynamical systems, and linear algebra. Academic Press 1974.
[K] M. Kanai: Differential-geometric studies on dynamics of geodesic and frame flows. Japan J. Math.  19 (1993), 1--30.
[KH] A. Katok and B. Hasselblatt: Introduction to the modern theory of dynamical systems. Encyclopedia of Mathematics and its Applications, 54. Cambridge University Press, Cambridge, 1995.
[P1] J. F. Plante: Anosov flows. American Journal of Mathematics  94 (1972), 729--754.
[P2] J. F. Plante: Homology of closed orbits of Anosov flows. Proceedings of the American Mathematical Society  37 (1973), 297--300.
[PT] J. F. Plante and W. P. Thurston: Anosov flows and the fundamental group. Topology  11 (1972), 147--150.
[S] S. Smale: Differentiable dynamical systems. Bulletin of the American Mathematical Society  73 (1967), 747--817.

[ Arbeitsgruppe Differentialgeometrie und Topologie]