Topological Methods in Hydrodynamics

Vladimir I. Arnold, Boris A. Khesin038794947X, 9780387949475, 9780387225890

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 achievements in (magneto)hydrodynamics and applications to hydrodynamic stability, dynamo theory and weather prediction. Topological methods in Hydrodynamics is the first monograph to treat topological, group-theoretic, and geometric problems of ideal hydrodynamics and magnetohydrodynamics from a unified point of view. 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.