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. I will demonstrate how this general approach works in the case of perturbations of systems with several asymptotically stable attractors, perturbations of an oscillator, of elastic systems, of the Landau-Lifshitz equation and its generalization. The same approach works also when PDEs with a small parameter are considered: the Neumann problem with a small parameter for second order elliptic PDEs will be considered.