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arXiv · 2207.02480

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

B. Lentjes·L. Spek·M. M. Bosschaert·Yu. A. Kuznetsov
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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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B. Lentjes, L. Spek, M. M. Bosschaert, Yu. A. Kuznetsov. 2022-07-06. Periodic Center Manifolds for DDEs in the Light of Suns and Stars. https://doi.org/10.1007/s10884-023-10289-9

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