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Topological Methods in Hydrodynamics

  • Book
  • © 2021

Overview

Authors:
  1. Vladimir I. Arnold

    1. Russian Academy of Sciences Steklov Mathematical Institute, Moscow, Russia

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    You can also search for this author in PubMed   Google Scholar

  2. Boris A. Khesin

    1. Department of Mathematics, University of Toronto, Toronto, Canada

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    You can also search for this author in PubMed   Google Scholar

  • The first and the only monograph to treat topological, group-theoretic, and geometric problems of ideal hydrodynamics and magneto-hydrodynamics from a unified point of view. It has become a classical book and the standard reference by now: Google Scholar includes nearly 1800 citations of this book
  • It includes over 70 figures, which helps the reader to "visualise", as opposed to "compute" hydrodynamics
  • It includes the survey of recent developments for the last 20 years in this now-flourishing field of topological and geometric hydrodynamics. The corresponding survey bibliography includes over 250 titles

Part of the book series: Applied Mathematical Sciences (AMS, volume 125)

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Table of contents (6 chapters)

  1. Front Matter

    Pages I-XX
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  2. Group and Hamiltonian Structures of Fluid Dynamics

    • Vladimir I. Arnold, Boris A. Khesin
    Pages 1-71

  3. Topology of Steady Fluid Flows

    • Vladimir I. Arnold, Boris A. Khesin
    Pages 73-125

  4. Topological Properties of Magnetic and Vorticity Fields

    • Vladimir I. Arnold, Boris A. Khesin
    Pages 127-205

  5. Differential Geometry of Diffeomorphism Groups

    • Vladimir I. Arnold, Boris A. Khesin
    Pages 207-274

  6. Kinematic Fast Dynamo Problems

    • Vladimir I. Arnold, Boris A. Khesin
    Pages 275-320

  7. Dynamical Systems with Hydrodynamic Background

    • Vladimir I. Arnold, Boris A. Khesin
    Pages 321-364

  8. Back Matter

    Pages 365-455
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Keywords

About this book

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 and Affiliations

  • Russian Academy of Sciences Steklov Mathematical Institute, Moscow, Russia

    Vladimir I. Arnold

  • Department of Mathematics, University of Toronto, Toronto, Canada

    Boris A. Khesin

About the authors

Vladimir Arnold (1937–2010) graduated from Moscow State University, Russia. While a student of Andrey Kolmogorov, Arnold showed in 1957 that any continuous function of several variables can be constructed with a finite number of two-variable functions, thereby completing the solution of Hilbert's thirteenth problem. Arnold worked at Moscow State University, the Steklov Mathematical Institute in Moscow, Russia, and at Paris Dauphine University, France. His groundbreaking contributions enriched such areas as the Kolmogorov–Arnold–Moser theory, dynamical systems, singularity theory, algebraic geometry, symplectic geometry and topology, differential equations, classical mechanics, topological Galois theory, and hydrodynamics. Arnold was also well known as a popularizer of mathematics, the author of many textbooks (such as the famous Mathematical Methods of Classical Mechanics), and outspoken critic of the Bourbaki style in mathematics.His awards include Shaw Prize, Wolf Prize, Lobachevsky Prize, Crafoord Prize, and many others.

Boris Khesin studied mathematics at Moscow State University, Russia. After obtaining his PhD in 1990 under the guidance of Vladimir Arnold, he spent several years at UC Berkeley and Yale University, USA, before moving to Toronto, Canada. Currently he is a Professor of Mathematics at the University of Toronto. His research interests include infinite-dimensional groups, Hamiltonian and integrable dynamics. The book "Topological Methods in Hydrodynamics" authored by Arnold and Khesin appears to be accepted as one of the main references in the field.



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