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Bifurcation of coisotropic invariant tori under locally Hamiltonian perturbations of integrable systems and nondegenerate deformation of symplectic structure

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Nonlinear Oscillations

Abstract

We study the bifurcation problem for a Cantor set of coisotropic invariant tori in the case where a Liouville-integrable Hamiltonian system undergoes locally Hamiltonian perturbations and, simultaneously, a deformation of the symplectic structure of the phase space. We consider a new case where the deformed symplectic structure generates a nondegenerate matrix of the Poisson brackets of action variables.

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Authors and Affiliations

  1. Shevchenko Kyiv University, Kyiv

    Yu.V. Loveikin & I. O. Parasyuk

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  1. Yu.V. Loveikin
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  2. I. O. Parasyuk
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Translated from Neliniini Kolyvannya, Vol. 9, No. 2, pp. 221–232, April–June, 2006.

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Loveikin, Y., Parasyuk, I.O. Bifurcation of coisotropic invariant tori under locally Hamiltonian perturbations of integrable systems and nondegenerate deformation of symplectic structure. Nonlinear Oscill 9, 215–225 (2006). https://doi.org/10.1007/s11072-006-0039-9

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  • DOI: https://doi.org/10.1007/s11072-006-0039-9

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