# Linear instability for periodic orbits of non-autonomous Lagrangian systems

@article{Portaluri2019LinearIF, title={Linear instability for periodic orbits of non-autonomous Lagrangian systems}, author={Alessandro Portaluri and Li Wu and Ran Yang}, journal={Nonlinearity}, year={2019}, volume={34}, pages={237 - 272} }

Inspired by the classical Poincaré criterion about the instability of orientation preserving minimizing closed geodesics on surfaces, we investigate the relation intertwining the instability and the variational properties of periodic solutions of a non-autonomous Lagrangian on a finite dimensional Riemannian manifold. We establish a general criterion for a priori detecting the linear instability of a periodic orbit on a Riemannian manifold for a (maybe not Legendre convex) non-autonomous…

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