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Symmetries of periodic solutions
for planar potential systems


Authors: Martin Golubitsky, Jian-Min Mao and Matthew Nicol
Journal: Proc. Amer. Math. Soc. 124 (1996), 3219-3228
MSC (1991): Primary 58F22, 34C25, 58F05
DOI: https://doi.org/10.1090/S0002-9939-96-03300-X
MathSciNet review: 1322926
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Abstract: In this article we discuss the symmetries of periodic solutions to Hamiltonian systems with two degrees of freedom in mechanical form. The possible symmetries of such periodic trajectories are generated by spatial symmetries (a finite subgroup of $\text {{\bf O(2)}})$, phase-shift symmetries (the circle group $\text {{\bf S}}^1)$, and a time-reversing symmetry (associated with mechanical form). We focus on the symmetries and structures of the trajectories in configuration space ($\mathbb R^2$), showing that special properties such as self-intersections and brake orbits are consequences of symmetry.


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Additional Information

Martin Golubitsky
Affiliation: Department of Mathematics, University of Houston, Houston, Texas 77204-3476
Email: mg@uh.edu

Jian-Min Mao
Affiliation: Department of Mathematics, Hong Kong University of Science and Technology, Hong Kong
Email: mamao@uxmail.ust.hk

Matthew Nicol
Affiliation: Department of Mathematics, UMIST, Manchester, United Kingdom
Email: m.nicol@umist.ac.uk

DOI: https://doi.org/10.1090/S0002-9939-96-03300-X
Received by editor(s): June 15, 1994
Additional Notes: Research supported in part by NSF Grant DMS-9101836, ONR Grant N00014-94-1-0317, and the Texas Advanced Research Program (003652037)
Communicated by: Hal L. Smith
Article copyright: © Copyright 1996 American Mathematical Society

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