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Topological Methods in Hydrodynamics

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First published in 1998 this unique monograph treats topological, group-theoretic, and geometric problems of ideal hydrodynamics and magneto-hydrodynamics from a unified point of view.It describes the necessary preliminary notions both in hydrodynamics and pure mathematics with numerous examples and figures. This book, now accepted as one of the main references in the field, is accessible to graduates as well as pure and applied mathematicians working in hydrodynamics, Lie groups, dynamical systems, and differential geometry. The updated second edition also contains a survey of recent developments in this now-flourishing field of topological and geometric hydrodynamics.

 

Authors: Arnold Vladimir I., Khesin Boris
Publisher: SPRINGER
Pages: 455
ISBN: 9783030742805
Cover: Paperback
Edition Number: 2
Release Year: 2021

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.

Arnold has been the advisor to more than 60 PhD students, and is famous for his seminar which thrived on his ability to discover new and beautiful problems. He is known all over the world for his textbooks which include the classics Mathematical Methods of Classical Mechanics, and Ordinary Differential Equations, as well as the more recent Topological Methods m Hydrodynamics written together with Boris Khesin, and Lectures on Partial Differential Equations.

Boris A. Khesin, University of Toronto, Toronto, ON, Canada

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