The calculation of periodic trajectories

Methods are presented for calculating classical periodic trajectories in a two-dimensional non-integrable potential problem. The main one is the monodromy method, which consists in refining an approximate solution by using a “once-around-the-trajectory” procedure. This can be done either for a given...

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Bibliographic Details
Published in:Annals of physics 1988-08, Vol.186 (1), p.95-110
Main Authors: Baranger, M., Davies, K.T.R., Mahoney, J.H.
Format: Article
Language:English
Subjects:
Classical and quantum physics: mechanics and fields
Classical mechanics of discrete systems: general mathematical aspects
Exact sciences and technology
Physics
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Summary:Methods are presented for calculating classical periodic trajectories in a two-dimensional non-integrable potential problem. The main one is the monodromy method, which consists in refining an approximate solution by using a “once-around-the-trajectory” procedure. This can be done either for a given period or for a given energy. Other methods proceed by searching on the initial conditions until the trajectory closes. We also discuss how to find new periodic milies, particularly branchings from already known families, and how to get started when no families are known.
ISSN:0003-4916
1096-035X
DOI:10.1016/S0003-4916(88)80018-6