Global dynamics for the Szekeres system with non-zero cosmological constant

The Szekeres system with cosmological constant term describes the evolution of the kinematic quantities for the Einstein field equations in dimension four. It is a Hamiltonian system (with Hamiltonian H). We restrict the dynamics on each one of the level surfaces H=h with h∈R and using the Poincaré compactification on R³ we analyze the global dynamics of the Szekeres system. It was known that the Szekeres system with cosmological constant term exhibits an attractor in the finite regime. Here we provide a new proof of the finite attractor and additionally we prove that also exhibits a repulsor in the finite regime, and that at infinity there is an attractor and a repulsor.