Integrable Hamiltonian Systems: Geometry, Topology, Classification

by A.V. Bolsinov, A.T. Fomenko

Overview

Integrable Hamiltonian systems have been of growing interest over the past 30 years and represent one of the most intriguing and mysterious classes of dynamical systems. This book explores the topology of integrable systems and the general theory underlying their qualitative properties, singularites, and topological invariants. The authors,

Product Details

ISBN-13:	9781134428991
Publisher:	CRC Press
Publication date:	02/25/2004
Sold by:	Barnes & Noble
Format:	eBook
Pages:	752
File size:	18 MB
Note:	This product may take a few minutes to download.

About the Author

Bolsinov, A.V.; Fomenko, A.T.

Table of Contents

Basic Notions. The Topology of Foliations on Two-Dimensional Surfaces Generated by Morse Functions. Rough Liouville Equivalence of Integrable Systems with Two Degrees of Freedom. Liouville Equivbalence of Integrable Systems with Two Degrees of Freedom. Orbital Classification of Integrable Systems with Two Degrees of Freedom. Classification of Hamiltonian Flows on Two-Dimensional Surfaces up to Topological Conjugacy. Smooth Conjugacy of Hamiltonian Flows on Two-Dimensional Surfaces. Orbital Classification of Integrable Hamiltonian Systems with Two Degrees of Freedom. The Second Step. Liouville Classification of Integrable Systems with Two Degrees of Freedom in Four-Dimensional Neighborhoods of Singular Points. Methods of Calculation of Topological Invariants of Integrable Hamiltonian Systems. Integrable Geodesic Flows on Two-Dimensional Surfaces. Liouville Classification of Integrable Geodesic Flows on Two-Dimensional Surfaces. Orbital Classification of Integrable Geodesic Flows on Two-Dimensional Surfaces. The Topology of Liouville Foliations in Classical Integrable Cases in Rigid Body Dynamics. Maupertuis Principle and Geodesic Equivalence.