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On critical level sets of some two degrees of freedom integrable Hamiltonian systems

 Printed: Feb 1998
  • Christine Médan
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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~\cite{fom} 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.
MSC Classifications: 70H05, 70H10, 58F14, 58F07 show english descriptions Hamilton's equations
unknown classification 70H10
unknown classification 58F14
unknown classification 58F07
70H05 - Hamilton's equations
70H10 - unknown classification 70H10
58F14 - unknown classification 58F14
58F07 - unknown classification 58F07

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