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The Melnikov technique and Arnold diffusion for a class of perturbed dissipative systems. (English) Zbl 0603.58037

Nonlinear problems in control and fluid dynamics, Proc. Conf., Berkeley/Calif. 1983, Lie Groups, Hist. Front. Appl., Ser. B 2, 397-403 (1984).
[For the entire collection see Zbl 0587.00027.]
The Melnikov technique was developed for testing the appearance of Arnold diffusion for nearly integrable Hamiltonian systems. The author is concerned with relaxing the rather severe requirement that both the unperturbed system and the perturbation terms must be of a Hamiltonian nature. The present paper offers a minor generalization in this direction. The perturbation terms of the system under consideration are Hamiltonian and assumed to be periodic in time. For the unperturbed system, however, n-1 of the degrees of freedom correspond to a superposition of nonlinear oscillators, whereas the final degree of freedom allows for dissipation and is assumed to possess a homoclinic orbit associated with a saddle point.
Reviewer: W.Sarlet

MSC:

37J40 Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol’d diffusion
57R70 Critical points and critical submanifolds in differential topology

Citations:

Zbl 0587.00027