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 equation. In particular, this collection covers the new topological obstructions to integrability, a new Morse-type theory of Bott integrals, and classification of bifurcations of the Liouville tori in integral 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.
Table of contents:
A T Fomenko. 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; G G Okuneva, Integrable Hamiltonian sytems in analytic dynamics and mathematical physics; A A Oshemkov, Fomenko invariants for the main integrable cases of the rigid body motion equations; A V Bolsinov, Methods of calculation of the Fomenko-Zieschang invariant; L S Polyakova, Topological invariants for some algebraic analogs of the Toda lattice; E N Selivanova, Topological classification of integrable Bott geodesic flows on the two-dimensional torus; T Z Nguyen, On the complexity of integrable Hamiltonian systems on three-dimensional isoenergy submanifolds; V V Trofimov, Symplectic connections and Maslov-Arnold characteristic classes; A T Fomenko and T Z Nguyen, Topological classification of integrable nondegenerate Hamiltonians on the isoenergy three-dimensional sphere; V V Kalashnikov (Junior), 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 S3, RP3, S1, X S2, and T3; A T Fomenko, Theory of rough classification of integrable nondegenerate Hamiltonian differential equations on four-dimensional manifolds. Application to classical mechanics.
Table of contents:
A T Fomenko. 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; G G Okuneva, Integrable Hamiltonian sytems in analytic dynamics and mathematical physics; A A Oshemkov, Fomenko invariants for the main integrable cases of the rigid body motion equations; A V Bolsinov, Methods of calculation of the Fomenko-Zieschang invariant; L S Polyakova, Topological invariants for some algebraic analogs of the Toda lattice; E N Selivanova, Topological classification of integrable Bott geodesic flows on the two-dimensional torus; T Z Nguyen, On the complexity of integrable Hamiltonian systems on three-dimensional isoenergy submanifolds; V V Trofimov, Symplectic connections and Maslov-Arnold characteristic classes; A T Fomenko and T Z Nguyen, Topological classification of integrable nondegenerate Hamiltonians on the isoenergy three-dimensional sphere; V V Kalashnikov (Junior), 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 S3, RP3, S1, X S2, and T3; A T Fomenko, Theory of rough classification of integrable nondegenerate Hamiltonian differential equations on four-dimensional manifolds. Application to classical mechanics.