We study the strong gravitational lensing properties of galaxy clusters obtained from N-body simulations with different kinds of dark energy (DE). We consider both dynamical DE, due to a scalar field self-interacting through Ratra—Peebles (RP) or supergravity (SUGRA) potentials, and DE with constant negative w=p/ρ=−1 (ΛCDM). We have 12 high-resolution lensing systems for each cosmological model with mass greater than 5.0 × 1014 h−1 M⊙. Using a ray shooting technique, we make a detailed analysis of the lensing properties of these clusters, paying particular attention to the number of arcs and their properties (magnification, length and width). We find that the number of giant arcs produced by galaxy clusters changes in a considerable way from ΛCDM models to dynamical dark energy models with an RP or SUGRA potential. These differences originate from the different epochs of cluster formation and from the non-linearity of the strong lensing effect. We suggest that strong lensing is one of the best tools to discriminate among different kinds of dark energ
