Periodic Center Manifolds for DDEs in the Light of Suns and Stars

Bram Lentjes*, Len Spek, Maikel M. Bosschaert, Yuri A. Kuznetsov

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

1 Citation (Scopus)
42 Downloads (Pure)

Abstract

In this paper, we prove the existence of a periodic smooth finite-dimensional center manifold near a nonhyperbolic cycle in classical delay differential equations by using the Lyapunov–Perron method. The results are based on the rigorous functional analytic perturbation framework for dual semigroups (sun–star calculus). The generality of the dual perturbation framework ensures that the results extend to a much broader class of evolution equations.

Original languageEnglish
JournalJournal of dynamics and differential equations
DOIs
Publication statusE-pub ahead of print/First online - 7 Aug 2023

Keywords

  • 2024 OA procedure
  • Delay differential equations
  • Dual perturbation theory
  • Nonhyperbolic cycles
  • Sun–star calculus
  • Center manifold theorem

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