Abstract

Polynomial four-dimensional symplectic mappings in the neighbourhood of a totally elliptic fixed point are considered. Such mappings can be derived as Poincare sections of flows of Hamiltonians with three degrees of freedom, and modelize a vast class of physical phenomena. Using the formalism of perturbative theory, a characterization of the ID tori that limit the stability domain when the linear frequencies are close to satisfy a low-order resonant conditions are worked out. The analytical results agree very well with numerical simulations. The case of a double resonance, which gives rise to OD tori (i.e. fixed points) is analysed. The perturbative series are used to work out the number of families and the related stability of these fixed points.

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