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

Bram Lentjes; Len Spek; Maikel M. Bosschaert; Yuri A. Kuznetsov

doi:10.48550/arXiv.2207.02480

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

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

Research output: Working paper › Preprint › Academic

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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 shows that the results extend to a much broader class of evolution equations.

Original language	English
Publisher	ArXiv.org
Number of pages	41
DOIs	https://doi.org/10.48550/arXiv.2207.02480
Publication status	Published - 6 Jul 2022

Keywords

math.DS
math.FA
34C25, 34K19, 37L10

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10.48550/arXiv.2207.02480Licence: CC BY

PreprintFinal published version, 576 KBLicence: CC BY

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Periodic Center Manifolds for DDEs in the Light of Suns and Stars
Lentjes, B., Spek, L., Bosschaert, M. M. & Kuznetsov, Y. A., Mar 2025, In: Journal of dynamics and differential equations. 37, p. 815–858 44 p.
Research output: Contribution to journal › Article › Academic › peer-review

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Cite this

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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 shows that the results extend to a much broader class of evolution equations. ",

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

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

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

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