Abstract

The Szekeres system with cosmological constant term describes the evolution of the kinematic quantities for Einstein field equations in R-4. 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-0 which indicate the integrability of the Hamiltonian system. We solve the Hamilton-Jacobi equation, and we reduce the Szekeres system from R-4 to an equivalent system defined in R-2. Global dynamics are studied where we find that there exists an attractor in the finite regime only for positive valued cosmological constant and I-0 -2.08. Otherwise, trajectories reach infinity. For I-0 > 0 the origin of trajectories in R-2 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 R-5. We see that the attractor at the finite regime in R-5 is related with the de Sitter universe for a positive cosmological constant.