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- W1650480413 abstract "It has been proved by S.L.Ziglin (1), for a large class of 2-degree-of-freedom (d.o.f) Hamiltonian sys- tems, 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. Hamil- tonians which exhibit, upon perturbation, subharmonic bi- furcations of resonant tori around an elliptic fixed point (2). 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 per- turbation is not Hamiltonian. tegrability of a system through the local analysis of the solution in the complex plane. Its origins can be found in Kowaleskaya's classical work and on the Painleve 's classification of second-order ordinary differential equations (see, e.g.(3)). However, for a long time, Kowaleskaya's work and Painleve 's the- ory were consider interesting, if not old fashioned, masterpieces in the theory of special functions and little attention was paid to them late 1970's, when it was noticed that they were intimately related to the theory of solitons. The various Painleve tests for ODEs which followed this discovery (3-5) are based on the formal existence of Laurent expansions for the solutions around the movable singularities of the solution in the complex plane. According to this approach one seeks to establish conditions such that all movable (i.e initial condi- tion dependent) singularities of the solutions of the equations of motion of the system dx" @default.
- W1650480413 created "2016-06-24" @default.
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- W1650480413 date "1999-03-23" @default.
- W1650480413 modified "2023-09-27" @default.
- W1650480413 title "Non-Integrability and Infinite Branching of Solutions of 2DOF Hamiltonian Systems in Complex Plane of Time ∗" @default.
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