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A Simple Proof of the Uniqueness of Periodic Orbits in the 1:3 Resonance Problem

Shiu-Nee Chow, Chengzhi Li and Duo Wang
Proceedings of the American Mathematical Society
Vol. 105, No. 4 (Apr., 1989), pp. 1025-1032
DOI: 10.2307/2047070
Stable URL: http://www.jstor.org/stable/2047070
Page Count: 8
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A Simple Proof of the Uniqueness of Periodic Orbits in the 1:3 Resonance Problem
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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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