POLYNOMIAL APPROXIMATIONS OF POINCARE MAPS FOR HAMILTONIAN-SYSTEMS .2.

In Paper I polynomial interpolating formulae of order 3 and 5 have bee n proposed and tested for transforming a non-linear differential Hamil tonian system into a map without having to integrate whole orbits as i n the well known Poincare return map technique. The precision of the c omputations increases drastically with the order of the polynomial fit which requires an extended amount of local information, i.e. informat ion about neighbouring points. The first part of the paper deals with another type of interpolation where the information, within the same a ccuracy, refers only to the nearest neighbours but takes into account gradient information. The results are in very good agreement with thos e obtained using an order 3 symmetrical interpolation formula well ins ide the phase space. Moreover the new method is more effective at the border of the phase space when compared with asymmetrical interpolatio n. The second part of the paper deals with higher dimensional mappings , i.e. mappings for Hamiltonian systems with 3 degrees of freedom.