# Linear instability of periodic orbits of free period Lagrangian systems

@inproceedings{Portaluri2021LinearIO, title={Linear instability of periodic orbits of free period Lagrangian systems}, author={Alessandro Portaluri and Li Wu and Ran Yang}, year={2021} }

In this paper we provide a sufficient condition for the linear instability of a periodic orbit for a free period Lagrangian system on a Riemannian manifold. The main result establish a general criterion for the linear instability of a maybe degenerate) periodic orbit admitting a orbit cylinder in terms to the parity of a suitable spectral index encoding the functional and symplectic property of the problem. AMS Subject Classification: 58E10, 53C22, 53D12, 58J30.

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