On the stability of Mañé critical hypersurfaces

Macarini, Leonardo; Paternain, Gabriel P.
November 2010
Calculus of Variations & Partial Differential Equations;Nov2010, Vol. 39 Issue 3/4, p579
Academic Journal
We construct examples of Tonelli Hamiltonians on $${\mathbb{T}^n}$$ (for any n ≥ 2) such that the hypersurfaces corresponding to the Mañé critical value are stable (i.e. geodesible). We also provide a criterion for instability in terms of closed orbits in free homotopy classes and we show that any stable energy level of a Tonelli Hamiltonian must contain a closed orbit.


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