| On the stability of Ma\~n\'e critical hypersurfaces (2009) | |||||||||
Abstract | |||||||||
| We construct examples of Tonelli Hamiltonians on $\T^n$ (for any $n\geq 2$) such that the hypersurfaces corresponding to the Ma\~n\'e 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.. Comment: 13 pages, 4 figures | |||||||||
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