Transverse intersections between invariant manifolds of doubly hyperbolic invariant tori, via the Poincaré-Mel'nikov method
Visualitza/Obre
transverse.pdf (481.7Kb) (Accés restringit)
Tipus de documentArticle
Data publicació2010-10
Condicions d'accésAccés restringit per política de l'editorial
Abstract
We consider a perturbation of an integrable Hamiltonian system having an equilibrium point of elliptic-hyperbolic type, having a homoclinic orbit. More precisely, we consider an (n + 2)-degree-of-freedom near integrable Hamiltonian with n centers and 2 saddles, and assume that the homoclinic orbit is preserved under the perturbation. On the center manifold near the equilibrium, there is a Cantorian family of hyperbolic KAM tori, and we study the homoclinic intersections between the stable and unstable manifolds associated to such tori. We establish that, in general, the manifolds intersect along transverse homoclinic orbits. In a more concrete model, such homoclinic orbits can be detected, in a first approximation, from nondegenerate critical points of a Mel’nikov potential. We provide bounds for the number of transverse homoclinic orbits using that, in general, the potential will be a Morse function (which gives a lower bound) and can be approximated by a trigonometric polynomial (which gives an upper bound).
Descripció
hyperbolic KAM tori - transverse homoclinic orbits - Melnikov method
CitacióDelshams, A. [et al.]. Transverse intersections between invariant manifolds of doubly hyperbolic invariant tori, via the Poincaré-Mel'nikov method. "Regular and chaotic dynamics", Octubre 2010, vol. 15, núm. 2-3, p. 222-236.
ISSN1560-3547
Versió de l'editorhttp://www.springerlink.com/content/967mw8482128j74h/
Fitxers | Descripció | Mida | Format | Visualitza |
---|---|---|---|---|
transverse.pdf![]() | 481.7Kb | Accés restringit |
Llevat que s'hi indiqui el contrari, els continguts d'aquesta obra estan subjectes a la llicència de Creative Commons:
Reconeixement-NoComercial-SenseObraDerivada 3.0 Espanya