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

Published online by Cambridge University Press:  20 November 2018

Christine Médan
Christine Médan*
Affiliation:
Laboratoire de Mathématiques Émile Picard Université Paul Sabatier 118, route de Narbonne 31062 Toulouse France
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Abstract

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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.

Keywords

70H0570H1058F1458F07
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 50 , Issue 1 , 01 February 1998 , pp. 134 - 151
Copyright
Copyright © Canadian Mathematical Society 1998

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