The point equivalence problem for ordinary differential equations of the second order

TL;DR

This paper applies E. Cartan's method to determine when second order ordinary differential equations are equivalent under point transformations, providing a systematic approach to classify such equations.

Contribution

It introduces a Cartan-based framework for solving the point equivalence problem for second order ODEs, advancing the understanding of their symmetry properties.

Findings

Established criteria for equivalence of second order ODEs

Developed a systematic Cartan method for classification

Enhanced understanding of symmetry transformations in ODEs

Abstract

We use E. Cartan's method to solve the problem of equivalence of the second order ordinary differential equations with respect to the pseudogroup of point transformations.