Nonautonomous Linear Systems: Exponential Dichotomy and its Applications

TL;DR

This paper introduces the theory of nonautonomous linear systems, focusing on exponential dichotomy and spectral theory, and extends linearization results within a nonautonomous framework for educational purposes.

Contribution

It provides an accessible introduction to exponential dichotomy and extends linearization results to nonautonomous systems, based on the authors' previous research.

Findings

Exponential dichotomy theory explained for nonautonomous systems

Linearization results adapted to nonautonomous frameworks

Educational approach based on multiple courses

Abstract

The first purpose of this work is to provide a friendly introduction to the theory of nonautonomous linear systems of ordinary differential equations, the property of exponential dichotomy and its corresponding spectral theory. The second purpose of this work is disseminate the linearization results carried out by the authors in a nonautonomous framework. The actual structure of this work is a consequence of several elective courses (2014, 2016, 2019, 2021 and 2023) carried out by the authors for undergraduate and graduated students at the Department of Mathematics of the Universidad de Chile. The monography assumes a good knowledge of multivariate calculus, linear algebra and ordinary differential equations.