## Access

You are not currently logged in.

Access JSTOR through your library or other institution:

## If You Use a Screen Reader

This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Journal Article

# 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

#### Select the topics that are inaccurate.

Cancel
Preview not available

## 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.

• 1025
• 1026
• 1027
• 1028
• 1029
• 1030
• 1031
• 1032