Three-Dimensional Manifolds of Constant Energy and Invariants of Integrable Hamiltonian Systems

  • Anatoly T. FomenkoEmail author
  • Kirill I. Solodskih
Part of the Understanding Complex Systems book series (UCS)


This paper is algebraic and topology study of the manifolds of constant energy of integrable Hamiltonian systems with two degrees of freedom. The Liouville foliation defines the topology of isoenergy manifold, but on any isoenergy manifold there are many non-equivalent Hamiltonian systems. We give some review of recent papers on homotopy invariants and their relation with Fomenko-Zieschang invariants. Also, we discuss relatively new results about Reidemeister torsion and applications in the theory of Hamiltonian systems. The last section is efficiency demonstration of Fomenko-Zieschang invariants in concrete mechanic system. Let us note that many known Hamiltonian systems have been investigated in terms of Fomenko-Zieschang invariants.


Integrable Hamiltonian Systems Liouville Foliation Isoenergy Manifold Concrete Mechanical Systems Saddle Atoms 
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Authors and Affiliations

  1. 1.Lomonosov Moscow State UniversityMoscowRussian Federation

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