Dynamics and chaos in the unified scalar field cosmology. II. System in a finite box

Abstract

We revisit the global dynamics of unified dark matter cosmological models and analyze it in a new dynamical system setting. In particular, by defining a suitable set of variables we obtain a bounded variable space, a feature that allows a better control of the critical elements of the system. First, we give a comprehensive cosmological interpretation of the critical points. Then, we turn our focus on particular representative trajectories with physically motivated initial conditions studied in the first paper of the series, and we discuss how the scale factor relates to the equation of state parameter. We review and complement these results in the light of the new variable approach by discussing the issue whether the system is chaotic or not.

Temporal and spatial chaos in the Kerr-AdS black hole in an extended phase space *

“…Chaos is a universal physical phenomenon in those nonlinear dynamical systems. Due to the intrinsic nonlin-P − V earity of Einstein 's general relativity theory, chaotic behavior is an important dynamics characteristic for such relativistic systems [18][19][20][21][22]. In the past few decades, more and more attention has been focused on the chaotic behavior in the black hole background [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37].…”