  We analyse $f(R)$ theories of gravity from a dynamical system perspective,
showing how the $R^2$ correction in Starobinsky's model plays a crucial role
from the viewpoint of the inflationary paradigm. Then, we propose a
modification of Starobinsky's model by adding an exponential term in the $f(R)$
Lagrangian. We show how this modification could allow to test the robustness of
the model by means of the predictions on the scalar spectral index $n_s$.
