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ALTERNATIVE REDUCTION BY STAGES OF KEPLERIAN SYSTEMS. POSITIVE, NEGATIVE, AND ZERO ENERGY

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dc.creatorFRANCISCO CRESPO CUTILLAS
dc.date2020
dc.date.accessioned2025-01-10T15:10:34Z
dc.date.available2025-01-10T15:10:34Z
dc.date.issued2020
dc.description.abstractTHIS WORK DEALS WITH THE FULL REDUCTION OF THE SPATIAL KEPLER SYSTEM FOR BOUNDED AND UNBOUNDED MOTIONS. PRECISELY, WE CONSIDER THE FOUR-DIMENSIONAL OSCILLATOR ASSOCIATED TO THE KEPLER SYSTEM AND CARRY OUT OUR PROGRAM IN THREE STAGES: AXIAL-AXIAL-ENERGY RATHER THAN ENERGY-AXIAL-AXIAL AS IS CUSTOMARY. THIS APPROACH REVEALS THE TRUE ROLE OF THE KS MAP AND THE BILINEAR RELATION. OUR DEVELOPMENT ALLOWS FOR A GLOBAL ANALYSIS AT EACH REDUCTION STAGE PROVIDING A COMPLETE DESCRIPTION OF EACH REDUCED SPACE. THE FIRST REDUCED SPACE IS DESCRIBED BY MEANS OF ONLY SIX INVARIANTS LEADING TO A NONSINGULAR SIX-DIMENSIONAL POISSON MANIFOLD. THEN, THE CLASSICAL BILINEAR RELATION IS REPLACED BY THE MOMENTUM MAP OF A GEOMETRIC REDUCTION. FURTHERMORE, THE SECOND REDUCED SPACE IS GIVEN AS THE PRODUCT OF TWO HYPERBOLOIDS AND HAS CONES AS SINGULAR STRATA. FOR THE LAST STAGE, WE DISTINGUISH AMONG THE POSSIBLE SIGN OF THE ENERGY. THE POSITIVE AND ZERO CASES BRING NEW NONCOMPACT REDUCED SPACES WHICH ARE DESCRIBED IN DETAIL.
dc.formatapplication/pdf
dc.identifier.doi10.1137/19M1264060
dc.identifier.issn1536-0040
dc.identifier.urihttps://repositorio.ubiobio.cl/handle/123456789/10779
dc.languagespa
dc.publisherSIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS
dc.relation.uri10.1137/19M1264060
dc.rightsPUBLICADA
dc.titleALTERNATIVE REDUCTION BY STAGES OF KEPLERIAN SYSTEMS. POSITIVE, NEGATIVE, AND ZERO ENERGY
dc.title.alternativeREDUCCIÓN ALTERNATIVA POR ETAPAS DE LOS SISTEMAS KEPLERIANOS. ENERGÍA POSITIVA, NEGATIVA Y CERO
dc.typeARTÍCULO
dspace.entity.typePublication
ubb.EstadoPUBLICADA
ubb.Otra ReparticionDEPARTAMENTO DE MATEMATICA
ubb.SedeCONCEPCIÓN
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