Topological and Orbital Analysis of Integrable Lagrange and Goryachev-Chaplygin Problems

  • O. E. Orël


A. T. Fomenko and A. V. Bolsinov [1994] obtained a new topological invariant for systems with two degrees of freedom, which classifies integrable Hamiltonian systems on constant-energy surfaces up to orbital equivalence. (Two smooth dynamical systems on manifolds M 1 and M 2 are called orbitally equivalent if there exists a homeomorphism from the first manifold onto the second one that transforms trajectories of the first system to trajectories of the second one with preservation of the orientation. More precisely, this is called continuous orbital equivalence; smooth orbital equivalence is defined analogously, with “homeomorphism” replaced by “diffeomorphism”. Notice that the transformation need not preserve the time parameter along trajectories.)


Bifurcation Diagram Symplectic Manifold Rotation Vector Integrable Problem Integrable Hamiltonian System 
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© Springer Japan 1997

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  • O. E. Orël

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