Publicación:
ALTERNATIVE ANGLE-BASED APPROACH TO THE KS-MAP. AN INTERPRETATION THROUGH SYMMETRY AND REDUCTION.

dc.creatorFRANCISCO CRESPO CUTILLAS
dc.date2018
dc.date.accessioned2025-01-10T15:02:03Z
dc.date.available2025-01-10T15:02:03Z
dc.date.issued2018
dc.description.abstractTHE KS MAP IS REVISITED IN TERMS OF AN S-1-ACTION IN (TH0)-H-* WITH THE BILINEAR FUNCTION AS THE ASSOCIATED MOMENTUM MAP. INDEED, THE KS TRANSFORMATION MAPS THE S-1-FIBERS RELATED TO THE MENTIONED ACTION TO SINGLE POINTS. BY MEANS OF THIS PERSPECTIVE A SECOND TWIN-BILINEAR FUNCTION IS OBTAINED WITH AN ANALOGOUS S-1-ACTION. WE ALSO SHOW THAT THE CONNECTION BETWEEN THE 4-D ISOTROPIC HARMONIC OSCILLATOR AND THE SPATIAL KEPLER SYSTEMS CAN BE DONE IN A STRAIGHTFORWARD WAY AFTER REGULARIZATION AND THROUGH THE EXTENSION TO 4 DEGREES OF FREEDOM OF THE EULER ANGLES, WHEN THE BILINEAR RELATION IS IMPOSED. THIS CONNECTION INCORPORATES BOTH BILINEAR FUNCTIONS AMONG THE VARIABLES. WE WILL SHOW THAT AN ALTERNATIVE REGULARIZATION SEPARATES THE OSCILLATOR EXPRESSED IN PROJECTIVE EULER VARIABLES. THIS SETTING TAKES ADVANTAGE OF THE TWO BILINEAR FUNCTIONS AND ANOTHER INTEGRAL OF THE SYSTEM INCLUDING THEM AMONG A NEW SET OF VARIABLES THAT ALLOWS TO CONNECT THE 4-D ISOTROPIC HARMONIC OSCILLATOR AND THE PLANAR KEPLER SYSTEM. IN ADDITION, OUR APPROACH MAKES TRANSPARENT THAT ONLY WHEN WE REFER TO RECTILINEAR SOLUTIONS, BOTH BILINEAR RELATIONS DEFINING THE KS TRANSFORMATIONS ARE NEEDED.
dc.formatapplication/pdf
dc.identifier.doi10.48550/arXiv.1711.08530
dc.identifier.issn1941-4897
dc.identifier.issn1941-4889
dc.identifier.urihttps://repositorio.ubiobio.cl/handle/123456789/10098
dc.languagespa
dc.publisherJournal of Geometric Mechanics
dc.relation.uri10.48550/arXiv.1711.08530
dc.rightsPUBLICADA
dc.titleALTERNATIVE ANGLE-BASED APPROACH TO THE KS-MAP. AN INTERPRETATION THROUGH SYMMETRY AND REDUCTION.
dc.title.alternativeENFOQUE ALTERNATIVO BASADO EN ÁNGULOS AL MAPA KS. UNA INTERPRETACIÓN A TRAVÉS DE LA SIMETRÍA Y LA REDUCCIÓN
dc.typeARTÍCULO
dspace.entity.typePublication
ubb.EstadoPUBLICADA
ubb.Otra ReparticionDEPARTAMENTO DE MATEMATICA
ubb.SedeCONCEPCIÓN
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