Non-slow-roll dynamics in $\alpha-$attractors
  In this paper we consider the $\alpha-$attractor model and study inflation
under a non-slow-roll dynamics. More precisely, we follow the approach recently
proposed by Gong and Sasaki \cite{Gong:2015ypa} by means of assuming
$N=N\left(\phi\right)$. Within this framework we obtain a family of functions
describing the local shape of the potential during inflation. We study a
specific model and find an inflationary scenario predicting an attractor at
$n_{s}\approx0.967$ and $r\approx5.5\times10^{-4}$. We further show that
considering a non-slow-roll dynamics, the $\alpha-$attractor model can be
broaden to a wider class of models that remain compatible with value of
$r<0.1$. We further explore the model parameter space with respect to large and
small field inflation and conclude that the inflaton dynamics is connected to
the $ \alpha- $ parameter, which is also related to the K\"ahler manifold
curvature in the supergravity (SUGRA) embedding of this model. We also comment
on the stabilization of the inflaton's trajectory.
