6 The Jacobi Bracket and the Lie Theory of Ordinary Differential Equations

Abstract

This chapter focuses on the Jacobi bracket and the Lie theory of ordinary differential equations. The “Lie theory” is interplay between the geometric interpretations of a system. The chapter discusses several local canonical form theorems for nonsingular vector fields and provides some indications of its importance in the Lie theory of ordinary differential equations. These theorems play a central role in the modern theory of ordinary differential equations.