Transformation Groups and Dynamical Systems

Many problems in mathematics concern with classification once a notion of equivalence is given in a class of mathematical objects. Classically, the theory of invariants proposes to study the orbits of a group action over a geometric object and the properties which remain stable under this action.
The aim of this CIMPA school is to give an introduction to different techniques in this context related with the study of holomorphic foliations and differential equations from a local and global viewpoint. More precisely, the courses will cover the following subjects:
differential Galois theory, algebraic properties of groups of local diffeomorphisms, automophism group of a foliation on a projective variety, algebraic and dynamical properties of birational maps of the complex proyective plane.