Geometrical theory of dynamical systems and fluid flows
Author(s)
Bibliographic Information
Geometrical theory of dynamical systems and fluid flows
（Advanced series in nonlinear dynamics, v. 23）
World Scientific, c2004
Available at / 17 libraries
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
DC22:515.39/K1282080013256
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Note
Includes bibliographical references and index
Description and Table of Contents
Description
This is an introductory textbook on the geometrical theory of dynamical systems, fluid flows, and certain integrable systems. The subjects are interdisciplinary and extend from mathematics, mechanics and physics to mechanical engineering, and the approach is very fundamental. The underlying concepts are based on differential geometry and theory of Lie groups in the mathematical aspect, and on transformation symmetries and gauge theory in the physical aspect. A great deal of effort has been directed toward making the description elementary, clear and concise, so that beginners will have an access to the topics.
Table of Contents
Mathematical Bases: Flows, Diffeomorphisms and Lie Groups Geometry of Surfaces in R3 Riemannian Geometry Dynamical Systems: Free Rotation of a Rigid Body Diffeomorphic Flows and KdV Equation on a Circle S1 Geometrical Theory of Chaos in a Hamiltonian Flows of an Ideal Fluid: Gauge Principle and Variational Formulation of Fluid Dynamics Flows of an Inviscid Incompressible Fluid Motion of a Vortex Filament Integrable Systems: Geometric Interpretations of Sine-Gordon Equation Geometric and Group-Theoretic Theory
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