Stability of equilibria and fixed points of conservative systems

Hildeberto E Cabral, Kenneth R Meyer
1999 Nonlinearity  
We consider the stability and instability of an equilibrium point of a Hamiltonian system of two degrees of freedom in certain resonance cases. We also consider the stability or instability of a fixed point of an area-preserving mapping in certain resonance cases. The stability criteria are established by Moser's invariant curve theorem and the instability is established by Chetaev's theorem.
doi:10.1088/0951-7715/12/5/309 fatcat:lp6ala45yvgjlpxtq6j7gcv5ha