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 Noethers theorem. The stability for the special solutions of the Szekeres system is studied and it is related with the with the Left or Right Painleve Series which describes the expansions.
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