Evolution of families of double- and triple-periodic orbits

Details Evolution of families of double- and triple-periodic orbits Evolution of families of double- and triple-periodic orbits

Jul 1985

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985cemec..36..257b&link_type=abstract

Celestial Mechanics (ISSN 0008-8714), vol. 36, July 1985, p. 257-271.

Mathematics

Dynamical Systems

5

Celestial Mechanics, Orbital Mechanics, Branching (Mathematics), Dynamical Systems, Taylor Series

Scientific paper

The author studies the evolution of the families of double- and triple-periodic orbits in a dynamical system that has closed zero velocity curves for arbitrarily large energies. He finds three interesting features: (1) the characteristic x = x(h) of the family of double periodic orbits divides the (x,h)-plane into two unconnected parts; (2) there is a sequence of sixteen closed characteristics, bifurcating from another one, each of them inside the previous one; (3) inside the innermost characteristic of that sequence there is a sequence of eight pairs of close characteristics which are not connected with any of the previous characteristics.

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