Optimalité systolique infinitésimale de l'oscillateur harmonique

Details Optimalité systolique infinitésimale de l'oscillateur harmonique Optimalité systolique infinitésimale de l'oscillateur harmonique

2010-03-31

arxiv.org/abs/1003.6004v1

Mathematics

Symplectic Geometry

5 pages

Scientific paper

We study the infinitesimal aspects of the following problem. Let H be a
Hamiltonian of \R^{2n} whose energy surface {H=1} encloses a compact starshaped
domain of volume equal to that of the unit ball in \R^{2n}. Does the energy
surface {H=1} carry a periodic orbit of the Hamiltonian system associated to H
with action less than or equal to \pi ?

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