A01=A.T. Fomenko
A01=A.V. Bolsinov
advanced integrable systems classification
Author_A.T. Fomenko
Author_A.V. Bolsinov
Bifurcation Diagram
Boundary Circles
Boundary Tori
Category=PBKJ
Category=PBM
curve
dynamical systems theory
eld
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Euler Case
foliation classification
geodesic flows
Hamiltonian Systems
Hamiltonian Vector Eld
Integrable Hamiltonian System
integral
Isoenergy Surfaces
Jacobi Problem
Klein Bottle
liouville
Liouville Foliation
Liouville Torus
map
Marked Molecule
Morse Functions
Morse theory applications
Orbital Invariants
Orbitally Equivalent
poincare
Reeb Graph
Riemannian Metric
rigid body dynamics
Rotation Function
Singular Leaf
Singular Point
Solid Torus
structure
symplectic
Symplectic Manifold
Symplectic Structure
topological invariants
torus
vector
Vector Eld
Product details
- ISBN 9780415298056
- Weight: 1161g
- Dimensions: 156 x 234mm
- Publication Date: 25 Feb 2004
- Publisher: Taylor & Francis Ltd
- Publication City/Country: GB
- Product Form: Hardback
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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, both of whom have contributed significantly to the field, develop the classification theory for integrable systems with two degrees of freedom. This theory allows one to distinguish such systems up to two natural equivalence relations: the equivalence of the associated foliation into Liouville tori and the usual orbital equaivalence. The authors show that in both cases, one can find complete sets of invariants that give the solution of the classification problem.
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 topological 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 geodesics 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.
Bolsinov, A.V.; Fomenko, A.T.
