I will consider long time influence of small deterministic and stochastic perturbations of various dynamical systems
and stochastic processes. The long time evolution of the perturbed system can be described by a motion in the cone
of invariant measures of the non-perturbed system. The set of extreme points of the cone can be often parametrized
by a graph or by an open book. The slow component of the perturbed system, is a process on this object.