Periodic solutions of differential equations with finite symmetry groups

Abstract

Periodic solutions of differential equations are essential in various scientific disciplines, from physics and engineering to biology and chemistry. This paper explores the notion of finite symmetry groups in the context of differential equations and their periodic solutions. We investigate how finite symmetry groups can be used to simplify the study of periodic solutions by identifying common patterns and simplifying the problem's structure. We provide examples of differential equations with finite symmetry groups and demonstrate how these symmetries lead to a reduced set of equations, which can significantly aid in the search for periodic solutions. By elucidating the interplay between symmetry and periodicity, this paper advances our understanding of periodic solutions and opens doors to more efficient techniques for their identification and analysis.