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The Isochronicity and Linearizability Problems

In: The Center and Cyclicity Problems

Author

Listed:
  • Valery Romanovski

    (University of Maribor, Center for Applied Mathematics & Theorectical Physics)

  • Douglas Shafer

    (University of North Carolina, Mathematics Dept.)

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.

Suggested Citation

  • Valery Romanovski & Douglas Shafer, 2009. "The Isochronicity and Linearizability Problems," Springer Books, in: The Center and Cyclicity Problems, chapter 0, pages 1-38, Springer.
    • Handle: RePEc:spr:sprchp:978-0-8176-4727-8_4
    DOI: 10.1007/978-0-8176-4727-8_4
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