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

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

doi:10.1007/s10884-023-10289-9

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 journal › Article › Academic › peer-review

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 language	English
Pages (from-to)	815–858
Number of pages	44
Journal	Journal of Dynamics and Differential Equations
Volume	37
Issue number	1
Early online date	7 Aug 2023
DOIs	https://doi.org/10.1007/s10884-023-10289-9
Publication status	Published - 2025

Bibliographical note

Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

Keywords

Center manifold theorem
Delay differential equations
Dual perturbation theory
Nonhyperbolic cycles
Sun–star calculus

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10.1007/s10884-023-10289-9

s10884-023-10289-9Final published version, 740 KBLicence: Taverne

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

keywords = "Center manifold theorem, Delay differential equations, Dual perturbation theory, Nonhyperbolic cycles, Sun–star calculus",

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PY - 2025

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AB - 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.

KW - Center manifold theorem

KW - Delay differential equations

KW - Dual perturbation theory

KW - Nonhyperbolic cycles

KW - Sun–star calculus

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ER -

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

Abstract

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Keywords

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