 |
Universität Augsburg
|
|
|
Universität Augsburg
|
|
Herr Fabian Ziltener
Korea Institute for Advanced Study / LMU
spricht am
Montag, 29. April 2013
um
16:00 Uhr
im
Raum 2004 (L1)
über das Thema:
| Abstract: |
| Consider a symplectic manifold $(M,\omega)$, a coisotropic submanifold $N$ of $M$, and a selfmap $\phi$ of $M$. A leafwise fixed point of $\phi$ is a point in $N$, which under $\phi$ is mapped to the isotropic leaf through itself. Symplectic manifolds naturally generalize phase space of classical mechanics. In this setting coisotropic submanifolds arise as energy level sets. Let $\phi$ be the time-one flow of a time-dependent perturbation of a given Hamiltonian function on $M$. Then a leafwise fixed point of $\phi$ is a point on a given energy level set whose trajectory is changed only by a phase shift, under the perturbation. The main result presented in this talk is that the number of leafwise fixed points is bounded below by the sum of the Betti numbers of $N$, provided that $\phi$ is not too far from the identity in the Hofer sense and some other conditions are satisfied. As an application, one obtains a symplectic capacity by considering the minimal actions of regular closed coisotropic submanifolds of a given symplectic manifold. A version of the capacity which is based on spheres, turns out to be discontinuous in dimension four. This answers a question by K. Cieliebak, H. Hofer, J. Latschev, and F. Schlenk. |
| Hierzu ergeht herzliche Einladung. |
| Kai Cieliebak |
Kaffee, Tee und Gebäck eine halbe Stunde vor Vortragsbeginn im Raum 2006 (L1).