Linearizability Problem of Resonant Degenerate Singular Point for Polynomial Differential Systems

Abstract EN

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 of p : −q resonant 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.