Optimalité systolique infinitésimale de l'oscillateur harmonique

Juan-Carlos Álvarez Paiva (1) , Florent Balacheff (1)

1 LPP - Laboratoire Paul Painlevé - UMR 8524

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 ?

Mots clés: Forme normale; oscillateur harmonique; volume systolique; système hamiltonien

Domaines: Géométrie symplectique [math.SG]; Systèmes dynamiques [math.DS]

Juan-Carlos Álvarez Paiva, Florent Balacheff. Optimalité systolique infinitésimale de l'oscillateur harmonique. 2010. ⟨hal-00467573⟩