Shadowing for infinite dimensional dynamics and exponential trichotomies

• Published in: Proceedings of the Royal Society of Edinburgh. Section A. Mathematics Vol. 151; no. 3; pp. 863 - 884
• Main Authors: Backes, Lucas, Dragičević, Davor
• Format: Journal Article
• Language: English
• Published: Edinburgh, UK Royal Society of Edinburgh Scotland Foundation 01.06.2021; Cambridge University Press
• Subjects: Banach spaces; Difference equations; Dynamics; Exponential trichotomies; 37C50; Nonautonomus systems; 34D10; 34D09; Shadowing; Nonlinear perturbations; Hyers–Ulam stability

Let $(A_m)_{m \in {\mathop Z}}$ be a sequence of bounded linear maps acting on an arbitrary Banach space X and admitting an exponential trichotomy and let $f_m:X \to X$ be a Lispchitz map for every $m\in {\mathop Z} $. We prove that whenever the Lipschitz constants of $f_m$, $m \in {\mathop Z} $, ar...