[Lower bounds of the splitting of the invariant manifolds]
Let m be an integer ⩾3, set for , and consider a badly approximable vector . Fix , and . We construct a sequence of Hamiltonian functions of , which converges to ℏ when , such that for each N the system generated by possesses a -dimensional hyperbolic invariant torus with fixed frequency vector , which admits a homoclinic point with splitting matrix of the form , with , where and .
Soit m un entier ⩾3, on pose pour , et on considère un vecteur mal approché par les rationnels (au sens de l'approximation simultanée). Fixons , et . Nous construisons une suite de Hamiltoniens de classe sur , qui converge vers ℏ lorsque , tels que le système engendré par laisse invariant un tore hyperbolique de vecteur fréquence fixe , qui admet un point homocline en lequel la matrice d'écart des variétés invariantes est de la forme , avec , où et .
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Jean-Pierre Marco 1
@article{CRMATH_2005__340_11_839_0, author = {Jean-Pierre Marco}, title = {Sur les bornes inf\'erieures de l'\'ecart des vari\'et\'es invariantes}, journal = {Comptes Rendus. Math\'ematique}, pages = {839--842}, publisher = {Elsevier}, volume = {340}, number = {11}, year = {2005}, doi = {10.1016/j.crma.2005.04.020}, language = {fr}, }
Jean-Pierre Marco. Sur les bornes inférieures de l'écart des variétés invariantes. Comptes Rendus. Mathématique, Volume 340 (2005) no. 11, pp. 839-842. doi : 10.1016/j.crma.2005.04.020. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.04.020/
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