The theory of dynamical systems, which in barest terms is the study of maps from a set to itself, permeates mathematics and science. It is used in diverse contexts, from proving the existence of solutions of equations to the modelling of complex natural phenomena. In more recent years dynamical methods have proven to be remarkably powerful in relation to problems in number theory, geometry and combinatorics which on the surface may seem to lack dynamical content. These various applications have lead to the consideration of dynamical systems preserving various types of additional structures. On the one hand this made the theory more applicable to different situations and also allowed on the other hand to improve the understanding of dynamical systems themselves.

This CIB program aims at gathering leading researchers in the various branches of dynamics for an exchange of ideas, techniques and problems in order to continue the advancement of this discipline in several directions and prepare the ground for further unexpected breakthroughs.