Nonlinear phenomena in solving Kepler's equation in the case of elliptic orbits.

Details Nonlinear phenomena in solving Kepler's equation in the case of elliptic orbits. Nonlinear phenomena in solving Kepler's equation in the case of elliptic orbits.

Jan 1998

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1998jnanu..34...21y&link_type=abstract

J. Nanjing Univ., Nat. Sci., Vol. 34, No. 1, p. 21 - 28

Physics

Two-Body Problem

Scientific paper

This paper discusses various nonlinear phenomena in solving Kepler's equation in the elliptic case by an improved Newtonian method with cubic convergence, which include multi-periodic points and chaotic belts, and strange attractors. Typical branches of period doubling occur with the increase of one of the parameters when the initial value is fixed. Especially, it is found that the region of non-convergence in the plane of parameters has a self-similar and fractal structure.

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