- 97-172 Vassilios M. Rothos, Tassos C. Bountis
- Non-Integrability and Infinite Branching of Solutions of 2DOF
Hamiltonian Systems in Complex Plane of Time
Apr 4, 97
(auto. generated ps),
of related papers
Abstract. It has been proved by S.L.Ziglin (1982), 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 (Bountis and Rothos, 1996).
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.