Jets of closed orbits of Mañé generic Hamiltonian flows

Abstract

We prove a perturbation theorem for the $k$-jets, $k\ge 2$, of the Poincaré map of a closed orbit of the Hamiltonian flow of a Tonelli Hamiltonian $H:T^{\ast }M\to \mathbb{R}$, on a closed manifold $M$. As a consequence we obtain Mañé generic properties of Hamiltonian and Lagrangian flows.

13 pages. To apear in Bulletin of the Brazilian Mathematical Society

References in corpus (1)

• Positive Topological Entropy for Magnetic Flows on Surfaces

Cited by in corpus (3)

• The second closed geodesic, the fundamental group, and generic Finsler metrics
• Billiards in generic convex bodies have positive topological entropy
• Waist theorems for Tonelli systems in higher dimensions