A Note on the Stability of Exponential Dichotomy of Linear Differential Equations

TL;DR

This paper provides an elementary functional analytic proof demonstrating the robustness of exponential dichotomy in linear differential equations on Banach spaces, emphasizing its stability under perturbations.

Contribution

It offers a new, simplified proof of the roughness of exponential dichotomy, enhancing understanding of stability in linear differential equations.

Findings

Exponential dichotomy is stable under perturbations.

Elementary proof simplifies existing complex arguments.

Applicable to differential equations on arbitrary Banach spaces.

Abstract

We present an elementary Functional Analytic proof of the roughness of Exponential Dichotomy of Ordinary Differential Equations (with exponential growth) on an arbitrary Banach Space.