A note on periodic differential equations

2009/08/19 by Mauro Patrão, Patrão, Mauro
Mathematics · Physics and Astronomy · #34A30 #34G10 #37B35 #Dynamical Systems (math.DS) #FOS: Mathematics #Numerical methods for differential equations #Quantum chaos and dynamical systems #advanced mathematical theories #math.DS #msc:34A30 #msc:34G10 #msc:37B35

paper · pdf · doi:10.48550/arxiv.0908.2833

10 pages

arxiv created 2009/08/19 · openalex publication_date 2009/08/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

Let F be a Banach space and L(F) be the set of all its bounded linear operators. In this note, we are interested in the asymptotic behavior (recurrence and chain recurrence) of the solution of the following initial value problem x'(t) = X(t)x(t), x(0) = x, where x ∈ F and the map t ↦ X(t) ∈ L(F) is a T-periodic continuous curve. This asymptotic behavior is related to the asymptotic behavior of the discrete-time flow on F generated by the invertible operator g ∈ L(F) given by the associated fundamental solution at time T.

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