# Symmetries and Singularities of the Szekeres System

## TL;DR

This paper investigates the symmetries and singularities of the Szekeres system, revealing its Lagrangian structure, conservation laws via Noether's theorem, and analyzing the stability of its solutions through Painlevé series expansions.

## Contribution

It introduces a novel analysis of the Szekeres system using group invariance and singularity methods, establishing its Lagrangian and conservation laws.

## Key findings

- The Szekeres system admits a Lagrangian formulation.
- Conservation laws are derived using Noether's theorem.
- Stability of solutions is linked to Painlevé series expansions.

## Abstract

The Szekeres system is studied with two methods for the determination of conservation laws. Specifically we apply the theory of group invariant transformations and the method of singularity analysis. We show that the Szekeres system admits a Lagrangian and the conservation laws that we find can be derived by the application of Noether's theorem. The stability for the special solutions of the Szekeres system is studied and it is related with the with the Left or Right Painlev\'e Series which describes the expansions.