Möbius fluid dynamics on the unitary groups

dc.creatorEmmanuele, Daniela Beatriz
dc.creatorSalvai, Marcos Luis
dc.creatorVittone, Francisco
dc.date2022-06-02
dc.date.accessioned2023-08-31T00:16:08Z
dc.date.available2023-08-31T00:16:08Z
dc.identifierhttp://hdl.handle.net/11336/202486
dc.identifierEmmanuele, Daniela Beatriz; Salvai, Marcos Luis; Vittone, Francisco; Möbius fluid dynamics on the unitary groups; Springer; Regular And Chaotic Dynamics; 27; 3; 2-6-2022; 333-351
dc.identifier1560-3547
dc.identifier1468-4845
dc.identifierCONICET Digital
dc.identifierCONICET
dc.identifier.urihttps://repositorioslatinoamericanos.uchile.cl/handle/2250/8543263
dc.descriptionWe study the nonrigid dynamics induced by the standard birational actions of the split unitary groups G=O_o(n,n), SU ( n,n) and Sp(n,n) on the compact classical Lie groups M = SO_n, U_n and Sp_n, respectively. More precisely, we study the geometry of G endowed with the kinetic energy metric associated with the action of G on M, assuming that M carries its canonical bi-invariant Riemannian metric and has initially a homogeneous distribution of mass. By the leastaction principle, force free motions (thought of as curves in G) correspond to geodesics of G. The geodesic equation may be understood as an inviscid Burgers equation with Möbius constraints. We prove that the kinetic energy metric on G is not complete and in particular not invariant, find symmetries and totally geodesic submanifolds of G and address the question under which conditions geodesics of rigid motions are geodesics of G. Besides, we study equivalences with the dynamics of conformal and projective motions of the sphere in low dimensions.
dc.descriptionFil: Emmanuele, Daniela Beatriz. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura; Argentina
dc.descriptionFil: Salvai, Marcos Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina
dc.descriptionFil: Vittone, Francisco. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura; Argentina
dc.formatapplication/pdf
dc.formatapplication/pdf
dc.languageeng
dc.publisherSpringer
dc.relationinfo:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1134/S1560354722030054
dc.relationinfo:eu-repo/semantics/altIdentifier/doi/10.1134/S1560354722030054
dc.rightsinfo:eu-repo/semantics/restrictedAccess
dc.rightshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subjectKINETIC ENERGY METRIC
dc.subjectSPLIT UNITARY GROUP
dc.subjectMÖBIUS ACTION
dc.subjectINVISCID BURGERS EQUATION
dc.subjectFORCE-FREE MOTION
dc.subjectNONROGOD DYNAMICS
dc.subjectUNITARY GROUP
dc.subjectMAXIMAL ISOTROPIC SUBSPACE
dc.subjecthttps://purl.org/becyt/ford/1.1
dc.subjecthttps://purl.org/becyt/ford/1
dc.titleMöbius fluid dynamics on the unitary groups
dc.typeinfo:eu-repo/semantics/article
dc.typeinfo:ar-repo/semantics/artículo
dc.typeinfo:eu-repo/semantics/publishedVersion


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