Polynomial approximation of Poincare maps for Hamiltonian systems

Details Polynomial approximation of Poincare maps for Hamiltonian systems Polynomial approximation of Poincare maps for Hamiltonian systems

Nov 1990

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1990a%26a...238..413f&link_type=abstract

Astronomy and Astrophysics (ISSN 0004-6361), vol. 238, no. 1-2, Nov. 1990, p. 413-423.

Statistics

Computation

5

Celestial Mechanics, Computational Astrophysics, Hamiltonian Functions, Nonlinear Systems, Polynomials, Liapunov Functions, Numerical Analysis, Perturbation Theory, Poincare Spheres, Taylor Series

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 Poincare return map technique. Piecewise polynomial maps are constructed by coarse-graining the phase surface of section into parallelograms using values of the Poincare maps at the vertices to define a polynomial approximation within each cell. The numerical experiments are in good agreement with both the real symplectic and Poincare maps. The agreement is better when the number of vertices and the order of the polynomial fit increase. Computations of Lyapunov characteristic exponents give a measure of how well the fit approximates the different maps.

Affiliated with

Also associated with

No associations

Rating

Polynomial approximation of Poincare maps for Hamiltonian systems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Polynomial approximation of Poincare maps for Hamiltonian systems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Polynomial approximation of Poincare maps for Hamiltonian systems will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-838535