Topological Classification Of Integrable Systems

Topological Classification of Integrable Systems

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 âeoebuilding blocksâe 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 bifurcation.

Topological Classification of Integrable Systems

New Results in the Theory of Topological Classification of Integrable Systems

This collection contains new results in the topological classification of integrable Hamiltonian systems. Recently, this subject has been applied to interesting problems in geometry and topology, classical mechanics, mathematical physics, and computer geometry. This new stage of development of the theory is reflected in this collection. Among the topics covered are: classification of some types of singularities of the moment map (including non-Bott types), computation of topological invariants for integrable systems describing various problems in mechanics and mathematical physics, construction of a theory of bordisms of integrable systems, and solution of some problems of symplectic topology arising naturally within this theory. A list of unsolved problems allows young mathematicians to become quickly involved in this active area of research.