A smooth trajectory classification of integrable Hamiltonian systems with two degrees of freedom

1995 ◽  
Vol 186 (1) ◽  
pp. 1-27 ◽  
Author(s):  
A V Bolsinov
Keyword(s):  
Hamiltonian Systems ◽  
Degrees Of Freedom ◽  
Integrable Hamiltonian Systems ◽  
Two Degrees Of Freedom ◽  
Trajectory Classification

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

1998 ◽  
Vol 50 (1) ◽  
pp. 134-151
Author(s):  
Christine Médan
Keyword(s):  
Large Class ◽  
Hamiltonian Systems ◽  
Geodesic Flow ◽  
Level Sets ◽  
Degrees Of Freedom ◽  
Critical Level ◽  
Integrable Hamiltonian Systems ◽  
Two Degrees Of Freedom ◽  
Lagrange Top

AbstractWe 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.

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