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Saddle singularities of complexity 1 of integrable Hamiltonian systems

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Abstract

Properties of saddle singularities of rank 0 and complexity 1 for integrable Hamiltonian systems are studied. An invariant (f n -graph) solving the problem of semi-local classification of saddle singularities of rank 0 for an arbitrary complexity was constructed earlier by the author. In this paper, a more simple form of the invariant for singularities of complexity 1 is obtained and some properties of such singularities are described in algebraic terms. In addition, the paper contains a list of saddle singularities of complexity 1 for systems with three degrees of freedom.

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Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Moscow State University, Leninskie Gory, Moscow, 119899, Russia

    A. A. Oshemkov

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  1. A. A. Oshemkov
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Original Russian Text © A.A. Oshemkov, 2011, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2011, Vol. 66, No. 2, pp. 10–19.

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Oshemkov, A.A. Saddle singularities of complexity 1 of integrable Hamiltonian systems. Moscow Univ. Math. Bull. 66, 60–69 (2011). https://doi.org/10.3103/S0027132211020021

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  • DOI: https://doi.org/10.3103/S0027132211020021

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