Linearizability Problem of Resonant Degenerate Singular Point for Polynomial Differential Systems

• Main Authors: Yusen Wu, Cui Zhang, Luju Liu
• Format: Article
• Language: English
• Published: Hindawi Limited 2012-01-01
• Series: Journal of Applied Mathematics
• Online Access: http://dx.doi.org/10.1155/2012/383282

The linearizability (or isochronicity) problem is one of the open problems for polynomial differential systems which is far to be solved in general. A progressive way to find necessary conditions for linearizability is to compute period constants. In this paper, we are interested in the linearizability problem of p : −q resonant degenerate singular point for polynomial differential systems. Firstly, we transform degenerate singular point into the origin via a homeomorphism. Moreover, we establish a new recursive algorithm to compute the so-called generalized period constants for the origin of the transformed system. Finally, to illustrate the effectiveness of our algorithm, we discuss the linearizability problems of 1 : −1 resonant degenerate singular point for a septic system. We stress that similar results are hardly seen in published literatures up till now. Our work is completely new and extends existing ones.