Publicación:
ON THE STABILITY OF RING RELATIVE EQUILIBRIA IN THE N-BODY PROBLEM ON S2 WITH HODGE POTENTIAL

dc.creatorJAIME EDUARDO ANDRADE BUSTOS
dc.date2023
dc.date.accessioned2025-01-10T15:40:05Z
dc.date.available2025-01-10T15:40:05Z
dc.date.issued2023
dc.description.abstractIN THIS PAPER, WE STUDY THE STABILITY OF THE RING SOLUTION OF THE N-BODY PROBLEM IN THE ENTIRE SPHERE S2 BY USING THE LOGARITHMIC POTENTIAL PROPOSED IN BOATTO ET AL. (2016, PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON. SERIES A. MATHEMATICAL, PHYSICAL AND ENGINEERING SCIENCES 472, 20160020) AND DRITSCHEL (2019, PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY OF LONDON. SERIES A. MATHEMATICAL, PHYSICAL AND ENGINEERING SCIENCES 377, 20180349), DERIVED THROUGH A DEFINITION OF CENTRAL FORCE AND HODGE DECOMPOSITION THEOREM FOR 1-FORMS IN MANIFOLDS. FIRST, WE CHARACTERIZE THE RING SOLUTION AND STUDY ITS SPECTRAL STABILITY, OBTAINING REGIONS (SPHERICAL CAPS) WHERE THE RING SOLUTION IS SPECTRALLY STABLE FOR 2?N?6 , WHILE, FOR N?7 , THE RING IS SPECTRALLY UNSTABLE. THE NONLINEAR STABILITY IS STUDIED BY REDUCING THE SYSTEM TO THE HOMOGRAPHIC REGULAR POLYGONAL SOLUTIONS, OBTAINING A 2-D.O.F. HAMILTONIAN SYSTEM, AND THEREFORE SOME CLASSIC RESULTS ON STABILITY FOR 2-D.O.F. HAMILTONIAN SYSTEMS ARE APPLIED TO PROVE THAT THE RING SOLUTION IS UNSTABLE AT ANY PARALLEL WHERE IT IS PLACED. ADDITIONALLY, THIS SYSTEM CAN BE REDUCED TO 1-D.O.F. BY USING THE ANGULAR MOMENTUM INTEGRAL, WHICH ENABLES US TO DESCRIBE THE PHASE PORTRAITS AND USE THEM TO FIND PERIODIC RING SOLUTIONS TO THE FULL SYSTEM. SOME OF THOSE SOLUTIONS ARE NUMERICALLY APPROXIMATED.
dc.formatapplication/pdf
dc.identifier.doi/10.4153/S0008414X23000123
dc.identifier.issn1496-4279
dc.identifier.issn0008-414X
dc.identifier.urihttps://repositorio.ubiobio.cl/handle/123456789/13098
dc.languagespa
dc.publisherCANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES
dc.relation.uri/10.4153/S0008414X23000123
dc.rightsPUBLICADA
dc.subjectSurfaces of constant curvature
dc.subjectspectral stability
dc.subjectring solution
dc.subjectreduced Hamiltonian
dc.subjectperiodic orbits
dc.subjectnonlinear stability
dc.subjectHamiltonian formulation
dc.titleON THE STABILITY OF RING RELATIVE EQUILIBRIA IN THE N-BODY PROBLEM ON S2 WITH HODGE POTENTIAL
dc.typeARTÍCULO
dspace.entity.typePublication
ubb.EstadoPUBLICADA
ubb.Otra ReparticionDEPARTAMENTO DE MATEMATICA
ubb.SedeCONCEPCIÓN
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