Efficient Method for Computing with Certainty Periodic Orbits on a Surface of Section

Details Efficient Method for Computing with Certainty Periodic Orbits on a Surface of Section Efficient Method for Computing with Certainty Periodic Orbits on a Surface of Section

Nov 2002

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002cemda..84..231p&link_type=abstract

Celestial Mechanics and Dynamical Astronomy, v. 84, Issue 3, p. 231-244 (2002).

Mathematics

Logic

3

Periodic Orbits, Poincaré Map, Surface Of Section, Dynamical Systems Photogravitational Problem, Fixed Points, Zeros Of Functions, Topological Degree, Newtons Method, Characteristic Bisection Method, Generalized Bisection Method

Scientific paper

We present an improved method for locating periodic orbits of a dynamical system of arbitrary dimension. The method first employs the characteristic bisection method (CBM) to roughly locate a periodic orbit, followed by the quadratically convergent Newton method to rapidly refine its position. The method is applied to the physically interesting example of the two degrees of freedom photogravitational problem, and shown to surpass the CBM algorithm and Newton's method alone.

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