Non-Integrability and Infinite Branching of Solutions of 2DOF Hamiltonian Systems in Complex Plane of Time

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dc.creatorRothos, Vassilios M.
dc.creatorBountis, Tassos C.
dc.date1999-03-23
dc.date.accessioned2026-07-07T02:35:41Z
dc.date.available2026-07-07T02:35:41Z
dc.descriptionIt has been proved by S.L.Ziglin, for a large class of 2-degree-of-freedom (d.o.f) Hamiltonian systems, that transverse intersections of the invariant manifolds of saddle fixed points imply infinite branching of solutions in the complex time plane and the non-existence of a second analytic integral of the motion. Here, we review in detail our recent results, following a similar approach to show the existence of infinitely-sheeted solutions for 2 d.o.f. Hamiltonians which exhibit, upon perturbation, subharmonic bifurcations of resonant tori around an elliptic fixed point. Moreover, as shown recently, these Hamiltonian systems are non-integrable if their resonant tori form a dense set. These results can be extended to the case where the periodic perturbation is not Hamiltonian.
dc.description9 pages, LaTeX, no figures. To appear in Nonlinear Phenomena in Complex Systems, 1999
dc.identifierhttps://arxiv.org/abs/chao-dyn/9903029
dc.identifierhttp://arxiv.org/abs/chao-dyn/9903029
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/15698
dc.subjectChaotic Dynamics
dc.titleNon-Integrability and Infinite Branching of Solutions of 2DOF Hamiltonian Systems in Complex Plane of Time
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