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Coisotropic Submanifolds of Symplectic Manifolds and Leafwise Fixed Points

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Speaker: 
Fabian Ziltener
Affiliation: 
U of Toronto/MPI
Date: 
Thu, 2010-07-15 15:00 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
MPI-Oberseminar

Coisotropic submanifolds generalize energy level sets of time-independent Hamiltonian systems. A leafwise fixed point of the time-one map of a time-dependent perturbation of the system corresponds to a trajectory for which the perturbation results in a phase shift. In this talk, I will illustrate this in the example of the harmonic oscillator, using a short computer animation. The main result of the talk is that under suitable hypotheses the number of leafwise fixed points is bounded below by the sum of the Betti numbers of the coisotropic submanifold.

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