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Focus-center problem of planar degenerate system
- Source :
-
Journal of Mathematical Analysis & Applications . Sep2008, Vol. 345 Issue 2, p934-940. 7p. - Publication Year :
- 2008
-
Abstract
- 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. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 0022247X
- Volume :
- 345
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Journal of Mathematical Analysis & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 32648900
- Full Text :
- https://doi.org/10.1016/j.jmaa.2008.05.030