Generic properties of closed orbits of Hamiltonian flows from Mañé's viewpoint

Ludovic Rifford (1, 2) , Rafael Ruggiero (3)

1 McTAO - Mathematics for Control, Transport and Applications
2 JAD - Laboratoire Jean Alexandre Dieudonné
3 departimento de matematica

We show the genericity from the viewpoint of Mañé of generic properties (as symplectic linear maps) of the differential of Poincaré maps of periodic orbits of Hamiltonians. Combining this result and the work of Oliveira we get a Kupka-Smale type theorem "à la Mañé" for regular energy levels of Tonelli Hamiltonians in compact manifolds. Our proof relies on techniques from geometric control theory.

Domaines: Systèmes dynamiques [math.DS]

Ludovic Rifford, Rafael Ruggiero. Generic properties of closed orbits of Hamiltonian flows from Mañé's viewpoint. International Mathematics Research Notices, 2011, 2012, pp.5246. ⟨hal-00923322⟩