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 Izv. Akad. Nauk SSSR Ser. Mat., 1991, Volume 55, Issue 4, Pages 747–779 (Mi izv987)

A bordism theory for integrable nondegenerate Hamiltonian systems with two degrees of freedom. A new topological invariant of higher-dimensional integrable systems

A. T. Fomenko

Abstract: Some new objects, bordisms of integrable systems, are found and studied. The classes of rigidly bordant systems form a nontrivial abelian group, which makes it possible to construct new integrable systems on the basis of previously known ones. Among the generators of this bordism group are known physical integrable systems, as, for example, the Lagrange system (from the dynamics of a heavy rigid body) and others. Moreover, a new topological invariant of systems with many degrees of freedom is also constructed. It turns out that two integrable systems are topologically equivalent if and only if their invariants coincide. In particular, it follows from this that the set of topological classes of integrable systems is discrete. The invariant can be effectively calculated for concrete integrable systems arising in physics and mechanics.

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English version:
Mathematics of the USSR-Izvestiya, 1992, 39:1, 731–759

Bibliographic databases:

UDC: 513.944
MSC: Primary 58F05, 57N10, 57M50, 57R90, 57R95; Secondary 55R50, 57N37, 58E15, 70E15, 70H99, 58F07, 55N15

Citation: A. T. Fomenko, “A bordism theory for integrable nondegenerate Hamiltonian systems with two degrees of freedom. A new topological invariant of higher-dimensional integrable systems”, Izv. Akad. Nauk SSSR Ser. Mat., 55:4 (1991), 747–779; Math. USSR-Izv., 39:1 (1992), 731–759

Citation in format AMSBIB
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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

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