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2012 Linearizability Problem of Resonant Degenerate Singular Point for Polynomial Differential Systems
Yusen Wu, Cui Zhang, Luju Liu
J. Appl. Math. 2012: 1-19 (2012). DOI: 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.


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Yusen Wu. Cui Zhang. Luju Liu. "Linearizability Problem of Resonant Degenerate Singular Point for Polynomial Differential Systems." J. Appl. Math. 2012 1 - 19, 2012.


Published: 2012
First available in Project Euclid: 14 December 2012

MathSciNet: MR2915735
zbMATH: 1248.34047
Digital Object Identifier: 10.1155/2012/383282

Rights: Copyright © 2012 Hindawi


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