Vladimir I. Arnold, Boris A. Khesin

Topological Methods in Hydrodynamics

• Gebundenes Buch

Produktbeschreibung

The first to examine topological, group-theoretic and geometric problems of ideal hydrodynamics and magnetohydrodynamics from a unified viewpoint, this book describes preliminary notions in hydrodynamics and pure mathematics with numerous examples and figures.

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This book develops the differential geometrical and topological points of view in hydrodynamics. It discusses interactions of hydrodynamics with a wide variety of mathematical domains such as theory of Lie groups, differential geometry, topology of knots, magnetic dynamo theory, calculus of variations and hamiltonian mechanics. The exposition contains extensive examples and figures, proofs of the main results, a survey of the recent achivements in (magneto) hydrodynamics and applications to hydrodynamic stability, dynamo theory and weather prediction.
The contents are 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.

Produktdetails

• Applied Mathematical Sciences 125
• Verlag: Springer / Springer New York / Springer, Berlin
• Artikelnr. des Verlages: 978-0-387-94947-5
• 1998.
• Seitenzahl: 396
• Erscheinungstermin: 13. April 1998
• Englisch
• Abmessung: 241mm x 160mm x 27mm
• Gewicht: 680g
• ISBN-13: 9780387949475
• ISBN-10: 038794947X
• Artikelnr.: 07158711

Autorenporträt

Vladimir Arnold is one of the great mathematical scientists of our time. He is famous for both the breadth and the depth of his work. His first mathematical work, which he did being a third-year student, was the solution of the 13th Hilbert problem about superpositions of continuous functions. His early work on KAM (Kolmogorov, Arnold, Moser) theory solved some of the outstanding problems of mechanics that grew out of fundamental questions raised by Poincare and Birkhoff based on the discovery of complex motions in celestial mechanics. In particular, the discovery of invariant tori, their dynamical implications, and attendant resonance phenomena is regarded today as one of the deepest and most significant achievements in the mathematical sciences. 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.

Inhaltsangabe

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.