Trapped Reeb orbits do not imply periodic ones
Event details
| Date | 04.03.2014 |
| Hour | 16:15 › 17:15 |
| Speaker | Nena Röttgen (Freiburg i. Br.) |
| Location |
MA A3 31
|
| Category | Conferences - Seminars |
Geometry and Dynamics Seminar
Abstract: The aim of the talk will be the construction of a contact form on R^{2n + 1} with n greater or equal to 2, yielding the standard contact structure, that is standard outside a compact set and induces a Reeb vector field with a compact invariant set, but no closed orbit. This gives a counterexample to a conjecture by H. Hofer. I will provide an overview of connected results. These will include a global Darboux Theorem by Eliashberg and Hofer showing that Reeb flows in higher dimension differ substantially from Reeb dynamics in dimension three.
Abstract: The aim of the talk will be the construction of a contact form on R^{2n + 1} with n greater or equal to 2, yielding the standard contact structure, that is standard outside a compact set and induces a Reeb vector field with a compact invariant set, but no closed orbit. This gives a counterexample to a conjecture by H. Hofer. I will provide an overview of connected results. These will include a global Darboux Theorem by Eliashberg and Hofer showing that Reeb flows in higher dimension differ substantially from Reeb dynamics in dimension three.
Practical information
- Expert
- Free
Organizer
- Martins Bruveris, Sonja Hohloch, Marc Troyanov