Linearizability Problem of Resonant Degenerate Singular Point for Polynomial Differential Systems

[摘要] 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 wayto find necessary conditions for linearizability is to compute period constants. In thispaper, we are interested in the linearizability problem ofp : −qresonant degeneratesingular point for polynomial differential systems. Firstly, we transform degeneratesingular point into the origin via a homeomorphism. Moreover, we establish a new recursive algorithm to compute the so-called generalized period constants for the originof the transformed system. Finally, to illustrate the effectiveness of our algorithm, wediscuss the linearizability problems of 1 : −1 resonant degenerate singular point for aseptic system. We stress that similar results are hardly seen in published literaturesup till now. Our work is completely new and extends existing ones.

[学科分类] 应用数学