The Isochronicity and Linearizability Problems
In the previous chapter we presented methods for determining whether the antisaddle at the origin of the real polynomial system (3.2) is a center or a focus, and more generally if the singularity at the origin of the complex polynomial system (3.4) is a center. In this chapter we assume that the singularity in question is known to be a center and present methods for determining whether or not it is isochronous, that is, whether or not every periodic orbit in a neighborhood of the origin has the same period. A seemingly unrelated problem is that of whether the system is linearizable (see Deӿnition 2.3.4) in a neighborhood of the origin. In fact, the two problems are intimately connected, as we will see in Section 4.2, and are remarkably parallel to the center problem.
KeywordsNormal Form Linearizability Problem Center Variety Polynomial System Component Versus
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