  We consider a minimally coupled scalar field with a monomial potential and a
perfect fluid in flat FLRW cosmology. We apply local and global dynamical
systems techniques to a new three-dimensional dynamical systems reformulation
of the field equations on a compact state space. This leads to a visual global
description of the solution space and asymptotic behavior. At late times we
employ averaging techniques to prove statements about how the relationship
between the equation of state of the fluid and the monomial exponent of the
scalar field affects asymptotic source dominance and asymptotic manifest
self-similarity breaking. We also situate the `attractor' solution in the
three-dimensional state space and show that it corresponds to the
one-dimensional unstable center manifold of a de Sitter fixed point, located on
an unphysical boundary associated with the dynamics at early times. By deriving
a center manifold expansion we obtain approximate expressions for the attractor
solution. We subsequently improve the accuracy and range of the approximation
by means of Pad\'e approximants and compare with the slow-roll approximation.
