Spectral comparison of compound cocycles generated by delay equations in Hilbert spaces

2023/02/06 by Mikhail Anikushin, Anikushin, Mikhail · 1 citation
Computer Science · Engineering · Mathematics · #34K08 #34K35 #37L15 #37L30 #37L45 #Advanced Differential Equations and Dynamical Systems #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Dynamics and Pattern Formation #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2302.02537

openalex publication_date 2023/02/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study linear cocycles generated by nonautonomous delay equations in a suitable Hilbert space and their extensions, called compound cocycles, to exterior powers. Using a recent version of the frequency theorem, we develop analytical techniques for comparing spectral properties, such as uniform exponential dichotomies, between such cocycles and semigroups generated by stationary equations. These methods are based on properties related to regularity and structure in PDEs associated with delay equations. In particular, the developed machinery leads to effective robust criteria that guarantee the absence of closed invariant contours on global attractors arising in nonlinear problems and are expected to ensure global stability.

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