  We develop a dynamical study of the sixth Painleve equation for all
parameters generalizing an earlier work for generic parameters. Here the main
focus of this paper is on non-generic parameters, for which the corresponding
character variety becomes a cubic surface with simple singularities and the
Riemann-Hilbert correspondence is a minimal resolution of the singular surface,
not a biholomorphism as in the generic case. Introducing a suitable
stratification on the parameter space and based on geometry of singular cubic
surfaces, we establish a chaotic nature of the nonlinear monodromy map of
Painleve VI and give a precise estimate for the number of its isolated periodic
solutions.
