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arXiv · 2602.17833

Periodic orbits of reversible Lagrangian systems without self-intersections and Ma\~n\'e genericity

Hans-Bert Rademacher
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Abstract

Bernard [3] showed that a Ma\~n\'e generic convex Hamiltonian has only non-degenerate periodic orbits on a given energy level. We show that one can use this result to prove that for a generic potential the prime periodic orbits of fixed energy of a Lagrangian system of classical type on a compact manifold of dimension $n\ge 3$ do not have self-intersections and do not intersect each other.

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Hans-Bert Rademacher. 2026-02-19. Periodic orbits of reversible Lagrangian systems without self-intersections and Ma\~n\'e genericity. https://arxiv.org/abs/2602.17833

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