We study the strong gravitational lensing properties of galaxy clusters
obtained from N-body simulations with different kind of Dark Energy (DE). We
consider both dynamical DE, due to a scalar field self--interacting through
Ratra-Peebles (RP) or SUGRA potentials, and DE with constant negative w=p/rho=
-1 (LCDM). We have 12 high resolution lensing systems for each cosmological
model with a mass greater than 5x10^{14} solar masses. Using a Ray Shooting
technique we make a detailed analysis of the lensing properties of these
clusters with particular attention to the number of arcs and their properties
(magnification, length and width). We found that the number of giant arcs
produced by galaxy clusters changes in a considerable way from LCDM models to
Dynamical Dark Energy models with a RP or SUGRA potentials. These differences
originate from the different epochs of cluster formation and from the
non-linearity of the strong lensing effect. We suggest the Strong lensing is
one of the best tool to discriminate among different kind of Dark Energy.Comment: 8 pages, 11 figures. Lensing map resolution improved and effects of
resolution discussed. One more RP model analysed. Accepted for publication by
MNRA