Generic properties of closed orbits for Lagrangian flows on surfaces

Details Generic properties of closed orbits for Lagrangian flows on surfaces Generic properties of closed orbits for Lagrangian flows on surfaces

2011-06-17

arxiv.org/abs/1106.3500v1

Mathematics

Dynamical Systems

11 pages

Scientific paper

We prove a local perturbation theorem for the $k$-jets of the Poincar\'e map
over a closed orbit of the flow of a Lagrangian system $ L: TM \to \R $ on a
closed surface $ M$. The perturbations consists of adding to the Lagrangian $ L
$ a $ C^\infty$-potential $ u: M \to \R $. Therefore we obtain generic
properties of closed orbits in the sense of Ma\~n\'e.

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