Point classification of the second order ODE's by Ruslan Sharipov and its application to Painleve equations

TL;DR

This paper reviews Ruslan Sharipov's classification of second order ODEs and demonstrates its application to analyzing Painleve equations, highlighting its historical significance and practical utility.

Contribution

It revisits and summarizes Sharipov's classification method and applies it to Painleve equations, showcasing its relevance and potential in differential equation analysis.

Findings

Sharipov's classification provides a systematic way to categorize second order ODEs.

Application to Painleve equations reveals new insights into their structure.

The review highlights the importance of historical methods in modern analysis.

Abstract

This is an review on the point classification of second order ODE's by Ruslan Sharipov. His works were published in 1997-1998 at the Electronic Archive at LANL and undeservedly forgotten. Last chapter is an application of this classification to the investigation of Painleve equations.