On the bifurcations of a certain family of periodic orbits

Details On the bifurcations of a certain family of periodic orbits On the bifurcations of a certain family of periodic orbits

Mar 1983

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983cemec..29..207h&link_type=abstract

Celestial Mechanics (ISSN 0008-8714), vol. 29, March 1983, p. 207-214.

Mathematics

9

Branching (Mathematics), Orbit Decay, Orbital Mechanics, Hamiltonian Functions, Numerical Integration, Periodic Functions, Potential Theory, Variational Principles

Scientific paper

Reference is made to numerical studies of a particular family of periodic orbits in a certain potential by Contopoulos and Zikides (1980) and Contopoulos (1981), where numerically successive values of the energy h at which the family becomes unstable are calculated. These studies showed that the ratio of successive values of h - h(esc), where h(esc) is the energy of escape, is approximately 9.22. It is shown here that the limiting ratio as h approaches h(esc) is exp(pi/the square root of 2) in this problem and that the limiting ratio for bifurcations of this type varies from one problem to another.

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