The Bifurcation of the Equatorial Periodic Orbit of the Planar Polynomial Vector Fields |
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| Authors: | Xin An Zhang Lan Sun Chen Zhao Jun Liang |
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| Affiliation: | (1) Department of Mathematics, Central China Normal University, Wuhan 430079, P. R. China;(2) Institute of Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, P. R. China;(3) Institute of Mathematics, Academy of Mathematics and System Sciences, Chinese Academy Sciences, Beijing 100080, P. R. China;(4) Department of Mathematics, Central China Normal University, Wuhan 430079, P. R. China |
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| Abstract: | In this paper, we have obtained the necessary and sufficient condition for the set of points at infinity on the plane R 2 to be a periodic orbit which is called an equatorial periodic orbit of a planar vector field X(x), and the formulae about the multiplicity of the equatorial periodic orbit of X(x). We have also proved that the main result of [9] is erroneous with regard to the formulae. This work is supported by the NSF of China |
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| Keywords: | Poincaré map Bifurcation Orthogonal projection |
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