 97172 Vassilios M. Rothos, Tassos C. Bountis
 NonIntegrability and Infinite Branching of Solutions of 2DOF
Hamiltonian Systems in Complex Plane of Time
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Apr 4, 97

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Abstract. It has been proved by S.L.Ziglin (1982), for a large class
of 2degreeoffreedom (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 nonexistence 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 infinitelysheeted solutions for 2 d.o.f.
Hamiltonians which exhibit, upon perturbation, subharmonic bifurcations
of resonant tori around an elliptic fixed point (Bountis and Rothos, 1996).
Moreover, as shown recently, these Hamiltonian systems are nonintegrable
if their resonant tori form a dense set.
These results can be extended to the case where
the periodic perturbation is not Hamiltonian.
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