Complex centers of polynomial differential equations
Date
2007-07-25
Authors
Alwash, Mohamad Ali M.
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University-San Marcos, Department of Mathematics
Abstract
We present some results on the existence and nonexistence of centers for polynomial first order ordinary differential equations with complex coefficients. In particular, we show that binomial differential equations without linear terms do not have complex centers. Classes of polynomial differential equations, with more than two terms, are presented that do not have complex centers. We also study the relation between complex centers and the Pugh problem. An algorithm is described to solve the Pugh problem for equations without complex centers. The method of proof involves phase plane analysis of the polar equations and a local study of periodic solutions.
Description
Keywords
Polynomial differential equations, Periodic solutions, Multiplicity, Centers, Pugh problem, Groebner bases
Citation
Alwash, M. A. M. (2007). Complex centers of polynomial differential equations. <i>Electronic Journal of Differential Equations, 2007</i>(101), pp. 1-15.
Rights
Attribution 4.0 International