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Topological Methods in Hydrodynamics : Applied Mathematical Sciences - Vladimir I. Arnold

Topological Methods in Hydrodynamics

Applied Mathematical Sciences

Hardcover Published: 5th August 1999
ISBN: 9780387949475
Number Of Pages: 376

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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.

Group and Hamiltonian Structures of Fluid Dynamics
Topology of Steady Fluid Flows
Topological Properties of Magnetic and Vorticity Fields
Differential Geometry of Diffeomorphism Groups
Kinematic Fast Dynamo Problems
Dynamical Systems with Hydrodynamical Background
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780387949475
ISBN-10: 038794947X
Series: Applied Mathematical Sciences
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 376
Published: 5th August 1999
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 23.5 x 15.5  x 2.54
Weight (kg): 0.7
Edition Number: 2