Hyperbolicity for Infinite Delayed Difference Equations

Speaker: Matheus Cunhas
Abstract: We show that the hyperbolicity of a linear delay-difference equation with infinite delay, expressed in terms of the existence of an exponential dichotomy, can be completely characterized by the hyperbolicity of a linear cocycle obtained from the solutions of the equation. As an appli-
cation of this characterization, we obtain several consequences: the extension of hyperbolicity to all equations in the invariant hull; the robustness of the existence of hyperbolicity for all equations in this hull under sufficiently small linear perturbations; and the equality of all spectra in the invariant hull.
Date: 29/10/2024 – 16:00
Room: 321 IMECC