We consider a class of Hamiltonians with three degrees of freedom that can be mapped into quasi-periodically driven pendulums. The purpose of this paper is to determine the threshold of the break-up of invariant tori with a specific frequency vector. We apply two techniques: the frequency map analysis and renormalization-group methods. The renormalization transformation acting on a Hamiltonian is a canonical change of coordinates which is a combination of a partial elimination of the irrelevant modes of the Hamiltonian and a rescaling of phase space around the considered torus. We give numerical evidence that the critical coupling at which the renormalization transformation starts to diverge is the same as the value given by the frequency map analysis for the break-up of invariant tori. Furthermore, we obtain by these methods numerical values of the threshold of the break-up of the last invariant torus.

Chandre, C., Laskar, J., Benfatto, G., & Jauslin, H.R. (2001). Determination of the threshold of the break-up of invariant tori in a class of three frequency Hamiltonian systems. PHYSICA D-NONLINEAR PHENOMENA, 154, 159-170 [10.1016/S0167-2789(01)00268-8].

Determination of the threshold of the break-up of invariant tori in a class of three frequency Hamiltonian systems

BENFATTO, GIUSEPPE;
2001

Abstract

We consider a class of Hamiltonians with three degrees of freedom that can be mapped into quasi-periodically driven pendulums. The purpose of this paper is to determine the threshold of the break-up of invariant tori with a specific frequency vector. We apply two techniques: the frequency map analysis and renormalization-group methods. The renormalization transformation acting on a Hamiltonian is a canonical change of coordinates which is a combination of a partial elimination of the irrelevant modes of the Hamiltonian and a rescaling of phase space around the considered torus. We give numerical evidence that the critical coupling at which the renormalization transformation starts to diverge is the same as the value given by the frequency map analysis for the break-up of invariant tori. Furthermore, we obtain by these methods numerical values of the threshold of the break-up of the last invariant torus.
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore MAT/07 - Fisica Matematica
English
Con Impact Factor ISI
Hamiltonian systems; Invariant tori; Renormalization Group
Chandre, C., Laskar, J., Benfatto, G., & Jauslin, H.R. (2001). Determination of the threshold of the break-up of invariant tori in a class of three frequency Hamiltonian systems. PHYSICA D-NONLINEAR PHENOMENA, 154, 159-170 [10.1016/S0167-2789(01)00268-8].
Chandre, C; Laskar, J; Benfatto, G; Jauslin, H
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2108/23733
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