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

Über die Autorin bzw. den Autor

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.

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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.