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1 results

  • On Critical Level Sets of Some two Degrees of Freedom Integrable Hamiltonian Systems

  • Christine Médan
  • Journal:
    Canadian Journal of Mathematics / Volume 50 / Issue 1 / 01 February 1998
    Published online by Cambridge University Press:
    20 November 2018, pp. 134-151
    Print publication:
    01 February 1998
    • Article
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  • We prove that all Liouville's tori generic bifurcations of a large class of two degrees of freedom integrable Hamiltonian systems (the so called Jacobi–Moser–Mumford systems) are nondegenerate in the sense of Bott. Thus, for such systems, Fomenko's theory [4] can be applied (we give the example of Gel'fand–Dikii's system). We also check the Bott property for two interesting systems: the Lagrange top and the geodesic flow on an ellipsoid.