Global portraits of nonminimal inflation
  We reconsider the dynamical systems approach to analyze inflationary universe
in the Jordan frame models of scalar field nonminimally coupled to curvature.
The adopted set of variables allows us to clearly distinguish between different
asymptotic states in the phase space, including the kinetic and inflationary
regimes. Inflation is realized as a heteroclinic trajectory originating either
at infinity from a nonhyperbolic asymptotic de Sitter point or from a regular
saddle de Sitter point. We also present a comprehensive picture of possible
initial conditions leading to sufficient inflationary expansion and show their
extent on the phase diagrams. In addition we comment on the slow roll
conditions applicable in the Jordan frame and show how they approximate the
leading inflationary "attractor solution". As particular examples we portrait
quadratic and quartic potential models and note that increasing the nonminimal
coupling diminishes the range of good initial conditions in the quadratic case,
but enlarges is in the quartic case.
