Linearizability Problem of Resonant Degenerate Singular Point for Polynomial Differential Systems. (8th May 2012)

• Record Type: Journal Article
• Authors: Wu, Yusen; Zhang, Cui; Liu, Luju
• Other Names: Guglielmi Nicola Academic Editor.
• Is Part Of: Journal of applied mathematics. Volume 2012(2012)
• Publication Date: 2012-05-08
• Subjects: Mathematics -- Periodicals; 519.05
• DOI: 10.1155/2012/383282
• Languages: English
• ISSNs: 1110-757X

Abstract

Abstract : 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.