Topological Methods in Hydrodynamics

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Springer Science & Business Media, Aug 5, 1999 - Mathematics - 376 pages
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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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Contents

lowledgments
1
The group setting of ideal magnetohydrodynamics
49
12 The NavierStokes equation from the group viewpoint
63
4 Asymptotic linking number
139
B Asymptotic crossing number of knots and links
155
7 Generalized helicities and linking numbers
166
8 Asymptotic holonomy and applications
184
Differential Geometry of Diffeomorphism Groups
195
Kinematic Fast Dynamo Problems 259
258
constructions
267
5 Dynamo exponents in terms of topological entropy
299
chain equations
331
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About the author (1999)

Arnol'd, Steklov Mathematical Institute

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