Linearizability problem of resonant degenerate singular point for polynomial differential systems (Q442907)

Summary: 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 a \(p:-q\) resonant degenerate singular point for polynomial differential systems. Firstly, we transform the 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.