Topological classification of integrable systems
著者
書誌事項
Topological classification of integrable systems
（Advances in Soviet mathematics, v. 6）
American Mathematical Society, c1991
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注記
Includes bibliographical references
内容説明・目次
内容説明
In recent years, researchers have found new topological invariants of integrable Hamiltonian systems of differential equations and have constructed a theory for their topological classification. Each paper in this important collection describes one of the 'building blocks' of the theory, and several of the works are devoted to applications to specific physical equations. In particular, this collection covers the new topological invariants of integrable equations, the new topological obstructions to integrability, a new Morse-type theory of Bott integrals, and classification of bifurcations of the Liouville tori in integrable systems. The papers collected here grew out of the research seminar 'Contemporary Geometrical Methods' at Moscow University, under the guidance of A. T. Fomenko, V. V. Trofimov, and A. V. Bolsinov. Bringing together contributions by some of the experts in this area, this collection is the first publication to treat this theory in a comprehensive way.
目次
The theory of invariants of multidimensional integrable Hamiltonian systems (with arbitrary many degrees of freedom). Molecular table of all integrable systems with two degrees of freedom by A. T. Fomenko Integrable Hamiltonian systems in analytic dynamics and mathematical physics by G. G. Okuneva Fomenko invariants for the main integrable cases of the rigid body motion equations by A. A. Oshemkov Methods of calculation of the Fomenko-Zieschang invariant by A. V. Bolsinov Topological invariants for some algebraic analogs of the Toda lattice by L. S. Polyakova Topological classification of integrable Bott geodesic flows on the two-dimensional torus by E. N. Selivanova On the complexity of integrable Hamiltonian systems on three-dimensional isoenergy submanifolds by T. Z. Nguyen Symplectic connections and Maslov-Arnold characteristic classes by V. V. Trofimov Topological classification of integrable nondegenerate Hamiltonians on the isoenergy three-dimensional sphere by A. T. Fomenko and T. Z. Nguyen Description of the structure of Fomenko invariants on the boundary and inside $Q$-domains, estimates of their number on the lower boundary for the manifolds $S^3$, $\Bbb R P^3$, $S^1\times S^2$, and $T^3$ by V. V. Kalashnikov, Jr. Theory of rough classification of integrable nondegenerate Hamiltonian differential equations on four-dimensional manifolds. Application to classical mechanics by A. T. Fomenko.
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