Abstract
Integrable hamiltonian systems are interesting because they are quite easy to understand and because many real systems are perturbations of them. When we have a perturbed system it is, in general, no longer integrable. The homoclinic phenomena are responsable for this lack of integrability. This is already seen in suitable perturbations of normal forms near a critical point. However some measure of this lack of integrability is interesting, because it tells us how far is the system of being integrable and, if we allow for some tolerance, we can decide when a non integrable system behaves like an integrable one for practical purposes. The same ideas lead us to a deep understanding of Arnold’s diffusion in systems of more than two degrees of freedom. If we add some dissipative perturbation there is a good chance to find complicated attractors. How and why they appear can be explained in terms of invariant manifolds.
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© 1985 D. Reidel Publishing Company
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Simö, C. (1985). Homoclinic Phenomena and Quasi-Integrability. In: Szebehely, V.G. (eds) Stability of the Solar System and Its Minor Natural and Artificial Bodies. NATO ASI Series, vol 154. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-5398-7_23
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DOI: https://doi.org/10.1007/978-94-009-5398-7_23
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