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.
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.
Accepted:
Published online:
Mots-clés : Tonelli Hamiltonian, Mather theory, Aubry set, weak KAM theory, Green bundles, tangent cones
Ke Zhang 1

@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/} }
TY - JOUR AU - Ke Zhang TI - On the tangent cones of Aubry sets JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2020 SP - 27 EP - 38 VL - 29 IS - 1 PB - Université Paul Sabatier, Toulouse UR - https://afst.centre-mersenne.org/articles/10.5802/afst.1621/ DO - 10.5802/afst.1621 LA - en ID - AFST_2020_6_29_1_27_0 ER -
%0 Journal Article %A Ke Zhang %T On the tangent cones of Aubry sets %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2020 %P 27-38 %V 29 %N 1 %I Université Paul Sabatier, Toulouse %U https://afst.centre-mersenne.org/articles/10.5802/afst.1621/ %R 10.5802/afst.1621 %G en %F AFST_2020_6_29_1_27_0
Ke Zhang. On the tangent cones of Aubry sets. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 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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