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Non-degeneracy of closed orbits for generic potentials
Patrick Bernard1
1PSL Research University, Université Paris-Dauphine, CEREMADE (UMR CNRS 7534), 75775 Paris Cedex 16, France
Journal de l’École polytechnique — Mathématiques, Volume 11 (2024), pp. 363-393

We prove that Mañé generic convex Hamiltonians have only non-degenerate periodic orbits on a given energy level. This result was stated, but not proved, in the literature.

On démontre qu’un hamiltonien convexe générique au sens de Mañé n’a que des orbites périodiques non dégénérées sur un niveau d’énergie donné. Ce résultat a déjà été énoncé, mais pas démontré, dans la littérature.

Received:
Accepted:
Published online:
DOI: 10.5802/jep.255
Classification: 70H12
Keywords: Hamiltonian systems, periodic orbits, generic properties, classical systems
Mots-clés : Systèmes hamiltoniens, orbites périodiques, propriétés génériques, systèmes classiques

Patrick Bernard  1

1 PSL Research University, Université Paris-Dauphine, CEREMADE (UMR CNRS 7534), 75775 Paris Cedex 16, France
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
Patrick Bernard. Non-degeneracy of closed orbits for generic potentials. Journal de l’École polytechnique — Mathématiques, Volume 11 (2024), pp. 363-393. doi: 10.5802/jep.255
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