Topological methods in hydrodynamics / Arnold, Vladimir I. (1998)

Topological methods in hydrodynamics [texte imprimé] / Arnold, Vladimir I., Auteur ; Khesin , Boris A., Auteur ; Khesin , Boris A.  . -  Vol.125 . - Berlin ; London ; Cham : Springer, 1998 . - XV-374 P. : ill. ; 24 cm. - (Applied mathematical sciences) .
ISBN : 978-0-387-94947-5
Bibliogr. p. 355 - 368 . Index p.369 - 374
Langues : Anglais (eng)

Mots-clés :	Hydrodynamique topologie
Index. décimale :	531.51 Lois de l'attraction universelle
Résumé :	Topological hydrodnamics is a young branch of mathematics studying topological features of fows with complicated trajectories, as well as their applications to fluid motions. it is situated at the crossroad of hydrodynamical sttability theody, riemannian and symplectic geometry, magnetohydrodynamics, theory of lie algebras and lie groups, knot theory, and dynamical systems. applications of this approach include topological classification of steady fluit flows, descriptions of the korteweg-de vries equation as a geodesic flow, and results on riemannian geometry of diffeomorphism groups, explaining, in particular, why longterm dynamical weather forecasts are not reliable.
Note de contenu :	Contents : 1. Group and hamiltonian structures of fluid dynamics 2. Topology of fsteady fluit flows 3. Topological properties of magnetic and vorticitc fields 4. Differnetial geomertry of diffeomorphism groups 5. Kinematic hast dynamo problems 6. Dynamical systems with hydrodynamical background