  We develop a formalism to characterize the redshift evolution of the dark
energy potential. Our formalism makes use of quantities similar to the
Horizon-flow parameters in inflation and is general enough that can deal with
multiscalar quintessence scenarios, exotic matter components, and higher order
curvature corrections to General Relativity. We show how the shape of the dark
energy potential can be recovered non parametrically using this formalism and
we present approximations analogous to the ones relevant to slow-roll
inflation. Since presently available data do not allow a non-parametric and
exact reconstruction of the potential, we consider a general parametric
description. This reconstruction can also be used in other approaches followed
in the literature (e.g., the reconstruction of the redshift evolution of the
dark energy equation of state w(z)). Using observations of passively evolving
galaxies and supernova data we derive constraints on the dark energy potential
shape in the redshift range 0.1 < z < 1.8. Our findings show that at the 1sigma
level the potential is consistent with being constant, although at the same
level of confidence variations cannot be excluded with current data. We
forecast constraints achievable with future data from the Atacama Cosmology
Telescope.
