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On the tangent cones of Aubry sets
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 29 (2020) no. 1, pp. 27-38.

Nous montrons que le cône paratangent de l’ensemble d’Aubry du Hamiltonien de Tonelli est contenu dans un cône borné par les fibrés de Green. Notre résultat améliore un résultat précédent de M.-C. Arnaud sur les cônes tangents des ensembles d’Aubry.

We show that the paratingent cone of the Aubry set of the Tonelli Hamiltonian is contained in a cone bounded by the Green bundles. Our result improves the earlier result of M.-C. Arnaud on tangent cones of the Aubry sets.

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Accepté le :
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DOI : https://doi.org/10.5802/afst.1621
Classification : 37J50,  37J05
Mots clés : Tonelli Hamiltonian, Mather theory, Aubry set, weak KAM theory, Green bundles, tangent cones
@article{AFST_2020_6_29_1_27_0,
     author = {Ke Zhang},
     title = {On the tangent cones of {Aubry} sets},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {27--38},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 29},
     number = {1},
     year = {2020},
     doi = {10.5802/afst.1621},
     language = {en},
     url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1621/}
}
Ke Zhang. On the tangent cones of Aubry sets. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 29 (2020) no. 1, pp. 27-38. doi : 10.5802/afst.1621. https://afst.centre-mersenne.org/articles/10.5802/afst.1621/

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