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RESEARCH PRODUCT
Determination of the threshold of the break-up of invariant tori in a class of three frequency Hamiltonian systems
Jacques LaskarHans-rudolf JauslinGiuseppe BenfattoCristel Chandresubject
PhysicsBreak-UpInvariant toriHamiltonian systems; Invariant tori; Renormalization GroupFOS: Physical sciencesStatistical and Nonlinear PhysicsTorusNonlinear Sciences - Chaotic DynamicsCondensed Matter PhysicsFrequency vectorHamiltonian systemRenormalizationThree degrees of freedomsymbols.namesakePhase spacesymbolsRenormalization GroupChaotic Dynamics (nlin.CD)Hamiltonian systems[PHYS.ASTR]Physics [physics]/Astrophysics [astro-ph]Hamiltonian (quantum mechanics)Mathematics::Symplectic GeometrySettore MAT/07 - Fisica MatematicaMathematical physicsdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2001-05-10 |