The equivariant moving frame method of third order differential equations

TL;DR

This paper applies the equivariant moving frame method to analyze the local equivalence of third order differential equations under fiber-preserving transformations, providing a systematic approach to classify such equations.

Contribution

It introduces the use of the equivariant moving frame method specifically for third order differential equations under a particular transformation group.

Findings

Developed a framework for the local equivalence problem

Derived invariants for third order differential equations

Provided classification criteria based on the invariants

Abstract

This paper is devoted to apply the equivariant moving frame method to study the local equivalence problem of third order ordinarily differential equation under the pseudo-group of fiber preserving transformations.