Bumpy metric theorem in the sense of Man{\'e} for non-convex Hamiltonians

TL;DR

This paper extends the bumpy metric theorem to non-convex Hamiltonians satisfying specific geometric conditions, broadening the scope of Mañe's theorem in Hamiltonian dynamics.

Contribution

It introduces a version of the bumpy metric theorem applicable to a class of non-convex Hamiltonians with particular geometric properties, which was not previously established.

Findings

Established a bumpy metric theorem for non-convex Hamiltonians.

Demonstrated the theorem under specific geometric conditions.

Extended the applicability of Mañe's theorem to new Hamiltonian classes.

Abstract

We prove a bumpy metric theorem in the sense of Ma\~{n}e for non-convex Hamiltonians that are satisfying a certain geometric property.