Topological Methods in Hydrodynamics

2. Auflage 2021
ISBN: 978-3-030-74277-5
Verlag: Springer International Publishing

Buch, Englisch, Band 125, 455 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 875 g

Reihe: Applied Mathematical Sciences

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.

Zielgruppe

Research

Autoren/Hrsg.

Khesin, Boris A.

Arnold, Vladimir I.

Fachgebiete

• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Kybernetik, Systemtheorie, Komplexe Systeme
• Technische Wissenschaften Maschinenbau | Werkstoffkunde Technische Mechanik | Werkstoffkunde Strömungslehre
• Mathematik | Informatik Mathematik Geometrie Dynamische Systeme
• Mathematik | Informatik Mathematik Mathematik Interdisziplinär Systemtheorie
• Mathematik | Informatik Mathematik Mathematik Allgemein
• Mathematik | Informatik EDV | Informatik Informatik Künstliche Intelligenz

Inhaltsverzeichnis

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.

Über Autor(innen)

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.