Linearizability Problem of Resonant Degenerate Singular Point for Polynomial Differential Systems

Yusen Wu, Cui Zhang and Luju Liu

Journal of Applied Mathematics, 2012, vol. 2012, 1-19

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.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:383282

DOI: 10.1155/2012/383282

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