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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A simple proof of the uniqueness of periodic orbits in the $ 1:3$ resonance problem


Authors: Shui-Nee Chow, Cheng Zhi Li and Duo Wang
Journal: Proc. Amer. Math. Soc. 105 (1989), 1025-1032
MSC: Primary 58F14; Secondary 58F21
DOI: https://doi.org/10.1090/S0002-9939-1989-0938908-6
MathSciNet review: 938908
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Abstract: In 1979, E. Horozov considered the versal deformation of a planar vector field which is invariant under a rotation through an angle $ 2\pi /3$ (with resonance of order 3). In his study, the most difficult part of the proof is on the uniqueness of limit cycles. In this note we give a simple and elementary (without the theory of algebraic geometry proof of the uniqueness of periodic orbits in the 1:3 resonance problem.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1989-0938908-6
Keywords: Bifurcation diagram, phase portrait, periodic orbit, Picard-Fuchs equation
Article copyright: © Copyright 1989 American Mathematical Society