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Symmetric Periodic Orbits in the Anisotropic Kepler Problem

Published online by Cambridge University Press:  12 April 2016

Josefina Casasaya  and
Jaume Llibre
Josefina Casasaya
Affiliation:
Facultat de Matemàtiques, Universitat de Barcelona, Barcelona 7, Spain
Jaume Llibre
Affiliation:
Secció de Matemàtiques, Facultat de Ciències, Universitat Autònoma de Barcelona, Bellaterra, Barcelona, Spain

Abstract

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The anisotropic Kepler problem has a group of symmetries with three generators; they are symmetries respect to zero velocity curve and the two axes of motion’s plane. For a fixed negative energy level it has four homothetic orbits. We describe the symmetric periodic orbits near these homothetic orbits. Full details and proofs will appear elsewhere (Casasayas-Llibre).

Type
Part IV - Periodic Orbits
Information
International Astronomical Union Colloquium , Volume 74: Dynamical Trapping and Evolution in the Solar System , 1983 , pp. 263 - 270
Copyright
Copyright © Reidel 1983

References

Casasayas, J. and Llibre, J., The global flow of the anisotropic Kepler problem (to appear).Google Scholar
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Devaney, R. (1981), Singularities in Classical Mechanical Systems, Progress in Mathematics vol. 10, Birkhäuser, Basel, pp. 211–333.Google Scholar
Gutzwiller, M. (1973), The anisotropic Kepler problem in two dimensions, J. Math. Phys. 14, pp. 139–152.Google Scholar