Topological Methods in Hydrodynamics
Topological hydrodynamics is a young branch of mathematics studying topological features of flows with complicated trajectories, as well as their applications to fluid motions. It is situated at the crossroad of hyrdodynamical stability theory, 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 fluid 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. Topological Methods in Hydrodynamics is the first monograph to treat topological, group-theoretic, and geometric problems of ideal hydrodynamics and magnetohydrodynamics for a unified point of view. The necessary preliminary notions both in hydrodynamics and pure mathematics are described with plenty of examples and figures. The book is accessible to graduate students as well as to both pure and applied mathematicians working in the fields of hydrodynamics, Lie groups, dynamical systems and differential geometry.
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The group setting of ideal magnetohydrodynamics
12 The NavierStokes equation from the group viewpoint
4 Asymptotic linking number
B Asymptotic crossing number of knots and links
7 Generalized helicities and linking numbers
8 Asymptotic holonomy and applications
Differential Geometry of Diffeomorphism Groups
Kinematic Fast Dynamo Problems 259
5 Dynamo exponents in terms of topological entropy
Phys. Rev. Lett. 92, 030406 (2004): v. Bodecker and Hornig - Link ...
V. Arnol'd and B. Khesin, Topological Methods in Hydrodynamics, Applied Mathematical Sciences Vol. 125 (Springer, New York, 1998). ...
link.aps.org/ doi/ 10.1103/ PhysRevLett.92.030406
Vladimir Igorevich Arnol'd (on his sixtieth birthday)
 Topological methods in hydrodynamics, Springer-Verlag, Berlin 1997 (Appl. Math. Series,. Vol. 125) (with ba Khesin); Russian transl., FAZIS, ...
www.turpion.org/ php/ full/ infoFT.phtml?journal_id=rm&
Vladimir I Arnold libri - I Libri dell'autore: Vladimir I Arnold ...
Topological Methods in Hydrodynamics · Topological Methods in Hydrodynamics di Vladimir I. Arnol'd, vi Arnold - Springer - April 1998. Prezzo: € 101.69 ...