caa a22 4500 475805240 CHVBK 20180406123745.0 cr unu---uuuuu 170329e20000201xx s 000 0 eng 10.1007/s003329910003 doi (NATIONALLICENCE)springer-10.1007/s003329910003 KAM-Type Theorem on Resonant Surfaces for Nearly Integrable Hamiltonian Systems [Elektronische Daten] [F. Cong, T. Küpper, Y. Li, J. You] Summary. : In this paper, we consider analytic perturbations of an integrable Hamiltonian system in a given resonant surface. It is proved that, for most frequencies on the resonant surface, the resonant torus foliated by nonresonant lower dimensional tori is not destroyed completely and that there are some lower dimensional tori which survive the perturbation if the Hamiltonian satisfies a certain nondegenerate condition. The surviving tori might be elliptic, hyperbolic, or of mixed type. This shows that there are many orbits in the resonant zone which are regular as in the case of integrable systems. This behavior might serve as an obstacle to Arnold diffusion. The persistence of hyperbolic lower dimensional tori has been considered by many authors [5], [6], [15], [16], mainly for multiplicity one resonant case. To deal with the mechanisms of the destruction of the resonant tori of higher multiplicity into nonhyperbolic lower dimensional tori, we have to deal with some small coefficient matrices that are the generalization of small divisors. Springer-Verlag New York Inc., 2000 Key words. Hamiltonian systems, resonant invariant tori, KAM-type theorem nationallicence Cong F. Department of Mathematics, Jilin University, Changchun 130023, People's Republic of China, CN aut Küpper T. Mathematisches Institut, Universität Köln, D-50931 Köln, Germany, DE aut Li Y. Department of Mathematics, Jilin University, Changchun 130023, People's Republic of China, CN aut You J. Department of Mathematics, Nanjing University, Nanjing 210093, People's Republic of China, CN aut Journal of Nonlinear Science Springer-Verlag 10/1(2000-02-01), 49-68 0938-8974 10:1<49 2000 10 332 https://doi.org/10.1007/s003329910003 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s003329910003 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Cong F. Department of Mathematics, Jilin University, Changchun 130023, People's Republic of China, CN aut NATIONALLICENCE 700 1- Küpper T. Mathematisches Institut, Universität Köln, D-50931 Köln, Germany, DE aut NATIONALLICENCE 700 1- Li Y. Department of Mathematics, Jilin University, Changchun 130023, People's Republic of China, CN aut NATIONALLICENCE 700 1- You J. Department of Mathematics, Nanjing University, Nanjing 210093, People's Republic of China, CN aut NATIONALLICENCE 773 0- Journal of Nonlinear Science Springer-Verlag 10/1(2000-02-01), 49-68 0938-8974 10:1<49 2000 10 332 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer