# Spectral invariants towards a Non-convex Aubry-Mather theory

@inproceedings{Vichery2014SpectralIT, title={Spectral invariants towards a Non-convex Aubry-Mather theory}, author={Nicolas Vichery}, year={2014} }

Aubry-Mather is traditionally concerned with Tonelli Hamiltonian (convex and super-linear). In \cite{Vi,MVZ}, Mather's $\alpha$ function is recovered from the homogenization of symplectic capacities. This allows the authors to extend the Mather functional to non convex cases. This article shows that the relation between invariant measures and the subdifferential of Mather's functional (which is the foundational statement of Mather) is preserved in the non convex case.
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## Mather theory and symplectic rigidity

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## topology

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## Symplectic intersections and invariant measures

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