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 bifurcations of the Liouville tori in integrable systems. The papers collected here grew out of the research seminar âeoeContemporary Geometrical Methodsâe 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