Periodic Center Manifolds for DDEs in the Light of Suns and Stars
Publication date
2025
Authors
Lentjes, Bram
Spek, Len
Bosschaert, Maikel
Kuznetsov, Yu.A.
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Advisors
Supervisors
Document Type
Article
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taverne
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, Taverne, Analysis
Citation
Lentjes, B, Spek, L, Bosschaert, M M & Kuznetsov, Y A 2025, 'Periodic Center Manifolds for DDEs in the Light of Suns and Stars', Journal of Dynamics and Differential Equations, vol. 37, no. 1, pp. 815–858. https://doi.org/10.1007/s10884-023-10289-9