  Using dynamical systems methods, we describe the evolution of a minimally
coupled scalar field and a Friedmann-Lemaitre-Robertson-Walker universe in the
context of general relativity, which is relevant for inflation and late-time
quintessence eras. Focussing on the spatially flat case, we examine the
geometrical structure of the phase space, locate the equilibrium points of the
system (de Sitter spaces with a constant scalar field), study their stability
through both a third-order perturbation analysis and Lyapunov functions, and
discuss the late-time asymptotics. As we do not specify the scalar field's
origin or its potential, the results are independent of the high-energy model.
