Chaos and the dynamical evolution of barred galaxies

2 pages, 4 figures, in the 5th International Conference "The Fabulous destiny of galaxies:Bridging past and present", (in press)The dynamical evolution of barred galaxies depends crucially on the fraction and their spacial distribution of chaotic orbits in them. In order to distinguish between the two kinds of orbits, we use the Smaller Alignment Index (SALI) method, a very powerful method which can be applied to problems of galactic dynamics. Using model potentials, and taking into account the full 3D distribution of matter, we discuss how the distribution of chaotic orbits depends on the main model parameters, like the mass of the various components and the bar axial ratio