A general mechanism of instability in Hamiltonian systems: skipping along a normally hyperbolic invariant manifold
Cita com:
hdl:2117/345184
Tipus de documentArticle
Data publicació2020
Condicions d'accésAccés obert
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Abstract
We describe a recent method to show instability in Hamiltonian systems. The main hypothesis of the method is that some explicit transversality conditions – which can be verified in concrete systems by finite calculations – are satisfied.
In particular, for several types of perturbations of integrable Hamiltonian systems, the hypothesis can be verified by just checking that some Melnikov-type integrals have non-degenerate zeros. This holds for Baire generic sets of perturbations in the Cr
-topology, for r¿[3,8)¿{¿}. Our method does not require that the unperturbed Hamiltonian system is convex, or that the perturbation is polynomial, which are non-generic properties.
Provided that the transversality conditions are verified, one concludes the existence of orbits which change the action coordinate by a quantity independent of the size of the perturbation. In fact, one can obtain orbits that follow any path in action space, up to an error decreasing with the size of the perturbation.
CitacióGidea, M.; De la Llave, R.; Martinez-seara, M. A general mechanism of instability in Hamiltonian systems: skipping along a normally hyperbolic invariant manifold. "Discrete & Continuous Dynamical Systems - A", 2020, vol. 40, núm. 12, p. 6795-6813.
ISSN1553-5231
Versió de l'editorhttps://www.aimsciences.org/article/doi/10.3934/dcds.2020166
Altres identificadorshttps://web.mat.upc.edu/tere.m-seara/articles/GideaLLSDCDS2020legal.pdf
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