Corpus ID: 117116896

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}
}
  • Nicolas Vichery
  • Published 2014
  • Mathematics
  • 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. We give applications in… CONTINUE READING

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