Publicación:
DYNAMICS OF AXIALLY SYMMETRIC PERTURBED HAMILTONIANS IN 1:1:1 RESONANCE

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dc.creatorDANTE CARRASCO OLIVERA
dc.creatorJOSÉ CLAUDIO VIDAL DÍAZ
dc.date2018
dc.date.accessioned2025-01-10T14:59:16Z
dc.date.available2025-01-10T14:59:16Z
dc.date.issued2018
dc.description.abstractWE STUDY THE DYNAMICS OF A FAMILY OF PERTURBED THREE-DEGREE-OF-FREEDOM HAMILTONIAN SYSTEMS WHICH ARE IN 1:1:1 RESONANCE. THE PERTURBATION CONSISTS OF AXIALLY SYMMETRIC CUBIC AND QUARTIC ARBITRARY POLYNOMIALS. OUR ANALYSIS IS PERFORMED BY NORMALISATION, REDUCTION AND KAM TECHNIQUES. FIRSTLY, THE SYSTEM IS REDUCED BY THE AXIAL SYMMETRY, AND THEN, PERIODIC SOLUTIONS AND KAM 3-TORI OF THE FULL SYSTEM ARE DETERMINED FROM THE RELATIVE EQUILIBRIA. NEXT, THE OSCILLATOR SYMMETRY IS EXTENDED BY NORMALISATION UP TO TERMS OF DEGREE 4 IN RECTANGULAR COORDINATES; AFTER TRUNCATION OF HIGHER ORDERS AND REDUCTION TO THE ORBIT SPACE, SOME RELATIVE EQUILIBRIA ARE ESTABLISHED AND PERIODIC SOLUTIONS AND KAM 3-TORI OF THE ORIGINAL SYSTEM ARE OBTAINED. AS A THIRD STEP, THE REDUCTION IN THE TWO SYMMETRIES LEADS TO A ONE-DEGREE-OF-FREEDOM SYSTEM THAT IS COMPLETELY ANALYSED IN THE TWICE REDUCED SPACE. ALL THE RELATIVE EQUILIBRIA TOGETHER WITH THE STABILITY AND PARAMETRIC BIFURCATIONS ARE DETERMINED. MOREOVER, THE INVARIANT 2-TORI (RELATED TO THE CRITICAL POINTS OF THE TWICE REDUCED SPACE), SOME PERIODIC SOLUTIONS AND THE KAM 3-TORI, ALL CORRESPONDING TO THE FULL SYSTEM, ARE ESTABLISHED. ADDITIONALLY, THE BIFURCATIONS OF EQUILIBRIA OCCURRING IN THE TWICE REDUCED SPACE ARE RECONSTRUCTED AS QUASI-PERIODIC BIFURCATIONS INVOLVING 2-TORI AND PERIODIC SOLUTIONS OF THE FULL SYSTEM.
dc.formatapplication/pdf
dc.identifier.doi10.1007/s00332-018-9449-y
dc.identifier.issn1432-1467
dc.identifier.issn0938-8974
dc.identifier.urihttps://repositorio.ubiobio.cl/handle/123456789/9879
dc.languagespa
dc.publisherJOURNAL OF NONLINEAR SCIENCE
dc.relation.uri10.1007/s00332-018-9449-y
dc.rightsPUBLICADA
dc.titleDYNAMICS OF AXIALLY SYMMETRIC PERTURBED HAMILTONIANS IN 1:1:1 RESONANCE
dc.title.alternativeDINÁMICA DE HAMILTONIANOS PERTURBADOS AXIALMENTE SIMÉTRICOS EN RESONANCIA 1:1:1
dc.typeARTÍCULO
dspace.entity.typePublication
ubb.EstadoPUBLICADA
ubb.Otra ReparticionDEPARTAMENTO DE MATEMATICA
ubb.Otra ReparticionDEPARTAMENTO DE MATEMATICA
ubb.SedeCONCEPCIÓN
ubb.SedeCONCEPCIÓN
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