Stewart-Lyth inverse problem

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Abstract
In this paper the Stewart-Lyth inverse problem is introduced. It consists of solving two nonlinear differential equations for the first slow-roll parameter and finding the inflaton potential. The equations are derived from the Stewart-Lyth equations for the scalar and tensorial perturbations produced during the inflationary period. The geometry of the phase planes transverse to the trajectories is analyzed, and conclusions about the possible behavior for general solutions are drawn.