The Isochronicity and Linearizability Problems

Valery Romanovski () and Douglas Shafer ()
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Valery Romanovski: University of Maribor, Center for Applied Mathematics & Theorectical Physics
Douglas Shafer: University of North Carolina, Mathematics Dept.

Chapter Chapter 4 in The Center and Cyclicity Problems, 2009, pp 1-38 from Springer

Abstract: 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.

Keywords: Normal Form; Linearizability Problem; Center Variety; Polynomial System; Component Versus (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-0-8176-4727-8_4

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DOI: 10.1007/978-0-8176-4727-8_4

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