Polynomial approximation of Poincaré maps for hamiltonian systems

Details Polynomial approximation of Poincaré maps for hamiltonian systems Polynomial approximation of Poincaré maps for hamiltonian systems

Feb 1996

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996em%26p...72...51f&link_type=abstract

Earth, Moon and Planets, Volume 72, Issue 1-3, pp. 51-56

Physics

Scientific paper

Different methods are proposed and tested for transforming a nonlinear differential system, and more particularly a hamiltonian one, into a map without having to integrate the whole orbit as in the well known Poincaré map technique. We construct piecewise polynomial maps by coarse-graining the phase surface of section into parallelograms using values of the Poincaré maps at the vertices to define a polynomial approximation within each cell. The numerical experiments are in good agreement with the standard map taken as a model problem. The agreement is better when the number of vertices and the order of the polynomial fit increase. The synthetic mapping obtained is not symplectic even if at vertices there is an exact interpolation. We introduce a second new method based on a global fitting . The polynomials are obtained using at once all the vertices and fitting by least square polynomes but in such a way that the symplectic character is not lost.

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