Optimalit\'e systolique infinit\'esimale de l'oscillateur harmonique
Abstract
We study the infinitesimal aspects of the following problem. Let H be a Hamiltonian of 2n whose energy surface H=1 encloses a compact starshaped domain of volume equal to that of the unit ball in 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 π ?
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