Artículo
Möbius fluid dynamics on the unitary groups
Fecha de publicación:
02/06/2022
Editorial:
Springer
Revista:
Regular And Chaotic Dynamics
ISSN:
1560-3547
e-ISSN:
1468-4845
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
We 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.
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Articulos(CIEM)
Articulos de CENT.INV.Y ESTUDIOS DE MATEMATICA DE CORDOBA(P)
Articulos de CENT.INV.Y ESTUDIOS DE MATEMATICA DE CORDOBA(P)
Citación
Emmanuele, 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
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