Article ID Journal Published Year Pages File Type
4620851 Journal of Mathematical Analysis and Applications 2008 7 Pages PDF
Abstract

In this paper we discuss how to determine a degenerate equilibrium of planar analytic systems to be focus-center type. A method of generalized normal sectors is used to determine orbits in exceptional directions near high degenerate equilibria. We obtain a sufficient and necessary condition for the existence of orbits going to origin in a generalized normal sector in class III. Thus, together with some criterions of orbits going to origin in a generic quasi-sector, we can characterize whether the degenerate equilibrium is of focus-center type in every case. The effectiveness of our methods is shown in an example which has a high degenerate equilibrium.

Related Topics
Physical Sciences and Engineering Mathematics Analysis