Non-degeneracy of closed orbits for generic potentials

TL;DR

This paper proves that for a broad class of convex Hamiltonians, all periodic orbits on a specific energy level are non-degenerate, filling a gap in the existing mathematical literature.

Contribution

It establishes the non-degeneracy of periodic orbits for Ma{} generic convex Hamiltonians on a given energy level, a previously unproven claim.

Findings

All periodic orbits are non-degenerate for Ma{} generic convex Hamiltonians.

The result confirms a conjecture stated but not proved in prior literature.

Provides a rigorous mathematical proof for the non-degeneracy property.

Abstract

We prove that Ma{\~n}{\'e} generic convex Hamiltonians have only non-degenerate periodic orbits on a given energy level. This result was stated, but not proved, in the literature.