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Infinitesimally stable and unstable singularities of 2-degrees of freedom completely integrable systems

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Abstract

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.

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  1. Dipartimento di Matematica Pura e Applicata, Università di Padova, Via Trieste 63, 35121, Padova, Italy

    A. Giacobbe

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Giacobbe, A. Infinitesimally stable and unstable singularities of 2-degrees of freedom completely integrable systems. Regul. Chaot. Dyn. 12, 717–731 (2007). https://doi.org/10.1134/S1560354707060123

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