[Instability times for perturbations of integrable analytic systems]
For a positive integer n and , we set . Given and we construct a sequence of analytic perturbations of the completely integrable Hamiltonian on , with unstable orbits for which we can estimate the time of drift in the action space. These functions are analytic on a fixed complex neighborhood V of , and if the time of drift of these orbits is smaller than for a fixed constant . Our unstable orbits pass close to a doubly resonant surface, so the result is almost optimal since the stability exponent for such orbits is .
Pour et on pose . Soient et . On construit une suite de Hamiltoniens analytiques sur un voisinage complexe V de , perturbations du Hamiltonien , qui possèdent des points pour lesquels le temps de dérive suivant les variables d'action est majoré par , où est une constante et . Les orbites considérées passent près de résonances doubles, le résultat est donc presque optimal puisque l'exposant de stabilité pour de telles orbites est .
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Jean-Pierre Marco 1
@article{CRMATH_2005__340_4_295_0, author = {Jean-Pierre Marco}, title = {Temps d'instabilit\'e pour les perturbations de syst\`emes int\'egrables analytiques}, journal = {Comptes Rendus. Math\'ematique}, pages = {295--300}, publisher = {Elsevier}, volume = {340}, number = {4}, year = {2005}, doi = {10.1016/j.crma.2004.12.019}, language = {fr}, }
Jean-Pierre Marco. Temps d'instabilité pour les perturbations de systèmes intégrables analytiques. Comptes Rendus. Mathématique, Volume 340 (2005) no. 4, pp. 295-300. doi : 10.1016/j.crma.2004.12.019. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.12.019/
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