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

TL;DR

This paper establishes the existence of periodic center manifolds near nonhyperbolic cycles in delay differential equations using advanced functional analysis, broadening applicability to various evolution equations.

Contribution

It introduces a novel approach employing the sun-star calculus to prove periodic center manifolds in DDEs, extending the theory to a wider class of evolution equations.

Findings

Existence of periodic smooth finite-dimensional center manifolds near nonhyperbolic cycles.

Application of the Lyapunov-Perron method within the sun-star calculus framework.

Framework extends to broader classes of evolution equations.

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.