  We propose a new parametrization of the background equations of motion
corresponding to (canonical) single-field models of inflation, which allows a
better understanding of the general properties of the solutions and of the
corresponding predictions in the inflationary observables. Based on the tools
of dynamical systems, the method suggests that inflation comes in two flavors:
power-law and de Sitter. Power-law inflation seems to occur for a restricted
type of potentials, whereas de Sitter inflation has a much broader
applicability. We also show a general perturbative method, by means of series
expansion, to solve the new equations of motion around the critical point of
the de Sitter type, and how the method can be used for arbitrary models of de
Sitter inflation. It is then argued that for the latter there are two general
classes of inflationary solutions, given in terms of the behavior of the
tensor-to-scalar ratio as a function of the number $N$ of $e$-folds before the
end of inflation: $r \sim N^{-1}$ (Class I), or $r \sim N^{-2}$ (Class II). We
give some examples of the two classes in terms of known scalar field
potentials, and compare their general predictions with constraints obtained
from observations.
