Topological Methods in Hydrodynamics: 125 (Applied Mathematical Sciences, 125) - Hardcover

Arnold, Vladimir I.; Khesin, Boris A.

 
9780387949475: Topological Methods in Hydrodynamics: 125 (Applied Mathematical Sciences, 125)

Synopsis

The first monograph to treat topological, group-theoretic, and geometric problems of ideal hydrodynamics and magnetohydrodynamics from a unified point of view. It describes the necessary preliminary notions both in hydrodynamics and pure mathematics with numerous examples and figures. The book is accessible to graduates as well as pure and applied mathematicians working in hydrodynamics, Lie groups, dynamical systems, and differential geometry.

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Product Description

Topological Methods in Hydrodynamics The first to examine topological, group-theoretic and geometric problems of ideal hydrodynamics and magnetohydrodynamics from a unified viewpoint, this book describes preliminary notions in hydrodynamics and pure mathematics with numerous examples and figures.

Synopsis

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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Other Popular Editions of the Same Title

9781475771534: Topological Methods in Hydrodynamics: 125 (Applied Mathematical Sciences, 125)

Featured Edition

ISBN 10:  1475771533 ISBN 13:  9781475771534
Publisher: Springer, 2013
Softcover