Integrable hamiltonian systems

Geometry, topology, classification

A.V. Bolsinov, A.T. Fomenko

730 pages, parution le 13/04/2004

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Résumé

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, singularities, and topological invariants.

The first part of the book systematically presents the general construction of these invariants, including many examples and applications. In the second part, the authors apply the general methods of the classification theory to the classical integrable problems in rigid body dynamics and describe their topologieal portraits, bifurcations of Liouville tori, and local and global topological invariants. They show how the classification theory helps find hidden isomorphisms between integrable systems and present as an example their proof that two famous systems-the Euler case in rigid body dynamics and the Jacobi problem of geodesies on the ellipsoid- are orbitally equivalent.

Integrable Hamiltonian Systems: Geometry, Topology, Classification offers a unique opportunity to explore important, previously unpublished results and acquire generally applicable techniques and tools that enable you to work with a broad class of integrable systems.

Sommaire

Basic notions
The topology of foliations on two-dimensional surfaces
Rough liouville equivalence of integrable systems with two degrees of freedom
Liouville equivalence 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 neighborhoods of singular points
Methods of calculation of topological invariants of integrable hamiltonian systems
Integrable geodesic flows on two-dimensional surfaces 409
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
Euler case in rigid body dynamics and jacobi problem about geodesics on the ellipsoid. Orbital isomorphism

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Chapman and Hall / CRC
Auteur(s)	A.V. Bolsinov, A.T. Fomenko
Parution	13/04/2004
Nb. de pages	730
Format	16 x 24
Couverture	Relié
Poids	1163g
Intérieur	Noir et Blanc
EAN13	9780415298056
ISBN13	978-0-415-29805-6