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arXiv 2207.024802022-07math.DSmath.FA

从 Suns 和 Stars 的视角看 DDE 的周期中心流形

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

B. Lentjes, L. Spek, M. M. Bosschaert, Yu. A. Kuznetsov

备注：: 41 pages
DOI：: 10.1007/s10884-023-10289-9

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AI总结：

本文利用 Lyapunov-Perron 方法和对偶半群的泛函分析扰动框架，证明了经典延迟微分方程中非双曲周期解附近存在周期光滑有限维中心流形，并指出该结果可推广至更广泛的演化方程类。

摘要：

本文利用 Lyapunov-Perron 方法，证明了经典延迟微分方程中非双曲周期解附近存在周期光滑有限维中心流形。该结果基于对偶半群（sun-star calculus）的严格泛函分析扰动框架。对偶扰动框架的普适性表明，结果可推广至更广泛的演化方程类。

英文摘要：

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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