Symmetries of Ordinary Differential Equations: A Short Introduction

Abstract: These lecture notes provide an introduction to the theory and application of symmetry methods for ordinary differential equations, building on minimal prerequisites. Their primary purpose is to enable a quick and self-contained approach for non-specialists; they are not intended to replace any of the monographs on this topic. The content of the notes lies "transversal" to most standard texts, since we put emphasis on autonomous ODEs of first order, which often play a relatively minor role. Moreover, we avoid the technical build-up involving jet spaces and prolongations of group actions.