Abstract

The Szekeres system with cosmological constant term describes the evolution of the kinematic quantities for Einstein field equations in R4. In this study, we investigate the behavior of trajectories in the presence of cosmological constant. It has been shown that the Szekeres system is a Hamiltonian dynamical system. It admits at least two conservation laws, h and I which indicate the integrability of the Hamiltonian system. We solve the Hamilton–Jacobi equation, and we reduce the Szekeres system from R4 to an equivalent system defined in R2. Global dynamics are studied where we find that there exists an attractor in the finite regime only for positive valued cosmological constant and I< - 2.08. Otherwise, trajectories reach infinity. For I> 0 the origin of trajectories in R2 is also at infinity. Finally, we investigate the evolution of physical properties by using dimensionless variables different from that of Hubble-normalization conducing to a dynamical system in R5. We see that the attractor at the finite regime in R5 is related with the de Sitter universe for a positive cosmological constant.