96-381 Wodnar K., Ichtiaroglou S., Meletlidou M.

Non-integrability and continuation of fixed points of 2n-dimensional perturbed twist mappings (163K, Postscript) Aug 22, 96

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Abstract. In this paper a simple criterion to prove non-integrability of symplectic, perturbed twist mappings in $2n$ dimensions is developed for sufficiently small perturbations. In addition an upper bound for the number of isolating integrals the system can possess is provided. A criterion for the analytic continuation of isolated periodic orbits in case of a small nonzero perturbation of twist maps is found. The evaluation of their linear stability character by obtaining a simplfied expression of the eigenvalues of the Jacobian matrix concludes the theoretical part. The theory is finally applied to a generalized standard map involving Jacobian elliptic functions.

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