Infinitesimally stable and unstable singularities of 2 degrees of freedom completely integrable systems
نویسنده
چکیده
In this article we give a list of 10 rank zero and 6 rank one singularities of 2 degrees of freedom completely integrable systems. Among such singularities, 14 are the singularities that satisfy a non-vanishing condition on the quadratic part, the remaining 2 are rank 1 singularities that play a role in the geometry of completely integrable systems with fractional monodromy. We describe which of them are stable and which are unstable under infinitesimal completely integrable deformations of the system. Mathematics Subject Classification: 55R55 Fiberings with singularities, 37J35 Completely integrable systems, topological structure of phase space, integration methods.
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