Topological Classification of Integrable Systems

Abstract

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.