Constructing integrating factor to distinguish between the center and the focus

doi:10.7523/j.issn.2095-6134.2018.05.001

›› 2018, Vol. 35 ›› Issue (5): 577-581.DOI: 10.7523/j.issn.2095-6134.2018.05.001

Constructing integrating factor to distinguish between the center and the focus

ZHI Junhai, CHEN Yufu

School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

Received:2017-05-02 Revised:2017-09-22 Online:2018-09-15
Supported by:
Supported by the National Natural Science Foundation of China(11271363)

Abstract

Abstract: In this paper we consider real differential systems which at singular points have purely imaginary eigenvalues. We show that the real invariant algebraic curves of the system are not identically zero in some deleted neighborhood U°(O). A method for seeking local first integrals or integrating factors is proposed, which can be used in determining the types of the equilibrium points.

Key words: invariant algebraic curve, first integral, integrating factor, equilibrium point

CLC Number:

ZHI Junhai, CHEN Yufu. Constructing integrating factor to distinguish between the center and the focus[J]. , 2018, 35(5): 577-581.

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Constructing integrating factor to distinguish between the center and the focus

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