Department Mathematik
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Prof. D. Kotschick

Seminar on Manifolds: Geometry of Anosov flows

The seminar will take place on Wednesdays, 11 AM to 1 PM starting on October 29th, in room E 39.
The papers by Anosov [A] and Smale [S] are good general references for all the early talks.

 
29. 10. D. Kotschick: Introduction, basic definitions and examples
05. 11. B. Hanke:  The geodesic flows of manifolds with negative curvature, [KH] 5.4+17.5+17.6, [AA] par 14 + Appendix 21
12. 11. E. Volkov/J. Iniotakis:  Stable and unstable foliations, openness/genericity 
[AA] par 15 + Appendix 22
19.+26. 11. O. Fabert:  Structural stability of: overtwisted disks [HS] 16.3;
Anosov systems [KH] 2.3, [AA] par 16 + Appendix 25, [S]
26.11.+3.12. T. Kuessner: Density of un-/stable manifolds [P1] 1.
10. 12. T. Vogel: Anosov flows with invariant transverse foliations [P1] 2.+3.
17. 12. J. Kedra: Anosov flows with invariant forms; closed orbits [P1] 4. + [P2]
07. 01. M. Hamilton: The Kanai connection [K]
14. 01. no talk!
21. 01. P. Ghiggini: Projectively Anosov flows and bi-contact structures
[ET] 2.2, [M], [EG]
28. 01. E. Volkov: Projectively Anosov flows with smooth un-/stable foliations [N]
04. 02. G. Bande/J. Kedra: Invariant two-forms [H]

References:
[A] D. V. Anosov: Geodesic flows on closed Riemann manifolds with negative curvature. Proc. of the Steklov Institute of Mathematics, No. 90 (1967). Amer. Math. Soc. Trans., Providence, R.I. 1969.
[AA] V. I. Arnold and A. Avez: Ergodic problems of classical mechanics. W. A. Benjamin, Inc., New York-Amsterdam 1968.
[ET] Y. M. Eliashberg and W. P. Thurston: Confoliations. Amer. Math. Soc., Providence, R.I. 1998.
[EG] J. Etnyre and R. Ghrist: Tight contact structures and Anosov flows. Top. and Appl. 124 (2002), 211--219.
[H] U. Hamenstädt: Invariant two-forms for geodesic flows. Math. Annalen  301 (1995), 677--698.
[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. Cambridge University Press, Cambridge, 1995.
[M] Y. Mitsumatsu: Anosov flows and non-Stein symplectic manifolds. Annales de l'Institut Fourier 45 (1995), 1407--1421.
[N] T. Noda: Projectively Anosov flows with differentiable (un)stable foliations. Annales de l'Institut Fourier 50 (2000), 1617--1647.
[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. Proc. Amer. Math. Soc.  37 (1973), 297--300.
[S] S. Smale: Differentiable dynamical systems. Bull. Amer. Math. Soc.  73 (1967), 747--817.

[ Arbeitsgruppe Differentialgeometrie und Topologie]