A simple proof of the uniqueness of periodic orbits in the $1:3$ resonance problem
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- by Shui-Nee Chow, Cheng Zhi Li and Duo Wang PDF
- Proc. Amer. Math. Soc. 105 (1989), 1025-1032 Request permission
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.References
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Additional Information
- © Copyright 1989 American Mathematical Society
- 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