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- catalog abstract "Topological hydrodynamics is a young branch of mathematics studying topological features of flows with complicated trajectories, as well as their applications to fluid motions. It is situated at the crossroad of hyrdodynamical stability theory, Riemannian and symplectic geometry, magnetohydrodynamics, theory of Lie algebras and Lie groups, knot theory, and dynamical systems. Applications of this approach include topological classification of steady fluid flows, descriptions of the Korteweg-de Vries equation as a geodesic flow, and results on Riemannian geometry of diffeomorphism groups, explaining, in particular, why longterm dynamical weather forecasts are not reliable. Topological Methods in Hydrodynamics is the first monograph to treat topological, group-theoretic, and geometric problems of ideal hydrodynamics and magnetohydrodynamics for a unified point of view. The necessary preliminary notions both in hydrodynamics and pure mathematics are described with plenty of examples and figures. The book is 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.".
- catalog contributor b10540632.
- catalog contributor b10540633.
- catalog created "1998.".
- catalog date "1998".
- catalog date "1998.".
- catalog dateCopyrighted "1998.".
- catalog description "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 -- References -- Index.".
- catalog description "Includes bibliographical references and index.".
- catalog description "Topological hydrodynamics is a young branch of mathematics studying topological features of flows with complicated trajectories, as well as their applications to fluid motions. It is situated at the crossroad of hyrdodynamical stability theory, Riemannian and symplectic geometry, magnetohydrodynamics, theory of Lie algebras and Lie groups, knot theory, and dynamical systems. Applications of this approach include topological classification of steady fluid flows, descriptions of the Korteweg-de Vries equation as a geodesic flow, and results on Riemannian geometry of diffeomorphism groups, explaining, in particular, why longterm dynamical weather forecasts are not reliable. Topological Methods in Hydrodynamics is the first monograph to treat topological, group-theoretic, and geometric problems of ideal hydrodynamics and magnetohydrodynamics for a unified point of view. The necessary preliminary notions both in hydrodynamics and pure mathematics are described with plenty of examples and figures. The book is 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.".
- catalog extent "xv, 374 p. :".
- catalog identifier "038794947X (hardcover : alk. paper)".
- catalog isPartOf "Applied mathematical sciences (Springer-Verlag New York Inc.) ; v. 125.".
- catalog isPartOf "Applied mathematical sciences ; 125".
- catalog issued "1998".
- catalog issued "1998.".
- catalog language "eng".
- catalog publisher "New York : Springer,".
- catalog subject "510 s 532/.5 21".
- catalog subject "Engineering.".
- catalog subject "Fluids.".
- catalog subject "Hydrodynamics.".
- catalog subject "Mathematics.".
- catalog subject "Physics.".
- catalog subject "QA1 .A647 vol. 125 QA911".
- catalog subject "Topology.".
- catalog tableOfContents "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 -- References -- Index.".
- catalog title "Topological methods in hydrodynamics / Vladimir I. Arnold, Boris A. Khesin.".
- catalog type "text".