  We estimate the Lyapunov times (characteristic times of predictability of
motion) in Quillen's models for the dynamics in the solar neighborhood. These
models take into account perturbations due to the Galactic bar and spiral arms.
For estimating the Lyapunov times, an approach based on the separatrix map
theory is used. The Lyapunov times turn out to be typically of the order of 10
Galactic years. We show that only in a narrow range of possible values of the
problem parameters the Galactic chaos is adiabatic; usually it is not slow. We
also estimate the characteristic diffusion times in the chaotic domain. In a
number of models, the diffusion times turn out to be small enough to permit
migration of the Sun from the inner regions of the Milky Way to its current
location. Moreover, due to the possibility of ballistic flights inside the
chaotic layer, the chaotic mixing might be even far more effective and quicker
than in the case of normal diffusion. This confirms the dynamical possibility
of Minchev and Famaey's migration concept.
