Abstract
We will discuss the onset of chaos in galactic models of two and three dimensions. We will consider integrable systems on which various types of perturbations are added. If the perturbation is strong enough, most orbits are chaotic. In systems of two degrees of freedom, the onset of chaos is due to infinite bifurcations, or infinite gaps. In systems of three degrees of freedom, we have transitions of complex instability, or inverse bifurcations. An increase of stochasticity in the form of "Arnold diffusion" may be due to changes in the interconnections of the various families of periodic orbits at a "collision of bifurcations".
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