 |
|
On critical level sets of some two degrees of freedom integrable Hamiltonian systems |
Canad. J. Math. 50(1998), 134-151
Published:1998-02-01
Printed: Feb 1998
Printed: Feb 1998
- Christine Médan
Abstract
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 - Hamilton's equations 70H10 - unknown classification 70H10 58F14 - unknown classification 58F14 58F07 - unknown classification 58F07 |