We study the complexification of the one-dimensional Newtonian particle in a monomial potential. We discuss cyclic motions on the associated Riemann surface, corresponding to a class of Newtonian dynamics in the plane. We also introduce the "center map", a one-parameter family of 2-d mappings describing the motion of the center of the circle, as a convenient representation of the cyclic dynamics. Computer experiments show a typical multifractal behavior with periodicity islands.
(joint work with P. G. Grinevich)
Contact A.P. Fordy (email: allan@maths.leeds.ac.uk ) for further details.
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