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Titolo:
On perturbed oscillators in 1-1-1 resonance: the case of axially symmetriccubic potentials
Autore:
Ferrer, S; Hanssmann, H; Palacian, J; Yanguas, P;
Indirizzi:
Univ Publ Navarra, Dept Matemat & Informat, Pamplona 31006, Spain Univ Publ Navarra Pamplona Spain 31006 & Informat, Pamplona 31006, Spain Univ Murcia, Dept Matemat Aplicada, E-30071 Murcia, Spain Univ Murcia Murcia Spain E-30071 Matemat Aplicada, E-30071 Murcia, Spain Rhein Westfal TH Aachen, Inst Reine & Angew Math, D-52056 Aachen, Germany Rhein Westfal TH Aachen Aachen Germany D-52056 , D-52056 Aachen, Germany
Titolo Testata:
JOURNAL OF GEOMETRY AND PHYSICS
fascicolo: 3-4, volume: 40, anno: 2002,
pagine: 320 - 369
SICI:
0393-0440(200201)40:3-4<320:OPOI1R>2.0.ZU;2-N
Fonte:
ISI
Lingua:
ENG
Soggetto:
RELATIVE EQUILIBRIA; HEILES PROBLEM; 3 DIMENSIONS; KAM-THEOREM; PERTURBATIONS; INTEGRABILITY; BIFURCATIONS; HAMILTONIANS; SYSTEMS; MOTION;
Keywords:
genuine resonance; axial symmetry; normal forms; reductions; invariants; relative equilibria; periodic orbits; invariant tori; reconstruction of the flow;
Tipo documento:
Article
Natura:
Periodico
Settore Disciplinare:
Physical, Chemical & Earth Sciences
Citazioni:
62
Recensione:
Indirizzi per estratti:
Indirizzo: Palacian, J Univ Publ Navarra, Dept Matemat & Informat, Pamplona 31006, Spain Univ Publ Navarra Pamplona Spain 31006 Pamplona 31006, Spain
Citazione:
S. Ferrer et al., "On perturbed oscillators in 1-1-1 resonance: the case of axially symmetriccubic potentials", J GEOM PHYS, 40(3-4), 2002, pp. 320-369

Abstract

Axially symmetric perturbations of the isotropic harmonic oscillator in three dimensions are studied. A normal form transformation introduces a second symmetry, after truncation. The reduction of the two symmetries leads to a one-degree-of-freedom system. To this end we use a special set of action-angle variables, as well as conveniently chosen generators of the ring of invariant functions. Both approaches are compared and their advantages and disadvantages are pointed out. The reduced flow of the normal form yields information on the original system. We analyse the 2-parameter family of (arbitrary) axially symmetric cubic potentials. This family has rich dynamics, displaying all local bifurcations of co-dimension one. With the exception of six ratios of the parameter values, the dynamical behaviour close to the origin turns out to be completely determined by the normal form of order 1. We also lay the ground for a further study at the exceptional ratios. (C) 2002 Elsevier Science B.V. All rights reserved.

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Documento generato il 18/01/20 alle ore 10:38:27