Topological Methods in Hydrodynamics

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.

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.