Introduction:
| |
Geometrically speaking, solutions of Dynamical Systems are organized according to hierarchies of invariant objects. This structure constitutes the skeleton of the dynamics in phase space. There is a long tradition of rigorous analytical results, starting with the work of H. Poincaré, dealing with existence and properties of such invariant objects (equilibria, periodic and quasi-periodic solutions, normally hyperbolic invariant manifolds, etc.). The use of analytical techniques is usually not enough to obtain a complete picture of this scenario in the study of a particular problem. In order to understand and rigorously characterize such objects, the corresponding dynamics on them and the connections between them, researchers started to develop algorithms for their effective computation in finite and infinite dimensional systems. In the last few years these efficient methods have led to methodologies for the rigorous validation of these objects with the assistance of computers (Computer-Assisted Proofs).
In this session we plan to bring together researchers of all these aspects of invariant manifolds. |
|