Symmetries of Ordinary Differential Equations: A Short Introduction

2019/11/04 by Sebastian Walcher, Walcher, Sebastian
Mathematics · Physics and Astronomy · #34-02 #34A05 #37C80 #Advanced Differential Equations and Dynamical Systems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #History and Overview (math.HO) #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1911.01053

openalex publication_date 2019/11/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• On differential equations in normal form

Related

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