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

Mathematics of Imaging & AI

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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.

Original language	English
Journal	Journal of dynamics and differential equations
DOIs	https://doi.org/10.1007/s10884-023-10289-9
Publication status	E-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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10.1007/s10884-023-10289-9

ArticleFinal published version, 750 KBLicence: Taverne

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title = "Periodic Center Manifolds for DDEs in the Light of Suns and Stars",

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

author = "Bram Lentjes and Len Spek and Bosschaert, {Maikel M.} and Kuznetsov, {Yuri A.}",

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AU - Bosschaert, Maikel M.

AU - Kuznetsov, Yuri A.

PY - 2023/8/7

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N2 - 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.

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 - 2024 OA procedure

KW - Delay differential equations

KW - Dual perturbation theory

KW - Nonhyperbolic cycles

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KW - Center manifold theorem

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

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Keywords

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

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

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