SS81 AIMS 2016 Meeting, Orlando, Florida, USA

Title:  Advances in Computer Assisted Proofs for Dynamical Systems and Differential Equations
Name: Affiliation: Country: Email Address:
Gianni Arioli
Politecnico di Milano
Jason Mireles-James
Florida Atlantic University
The last 20 years have seen a significant development of techniques for computer assisted proofs in dynamical systems theory. Such techniques are used to prove the existence of solutions of ordinary and partial differential equations, and to study invariant sets in a mathematically rigorous way using the computer. These techniques use two main fundamental approaches: one is based on topological tools, the other on functional analysis. The first approach, when applied to differential equations, relies on the development of efficient rigorous integrators and studies how sets in phase space map across one another. The second approach relies on transforming the equations into fixed points problems in some functional space. These approaches are somehow complementary, and the aim of this session is to discuss recent advances in order to learn how to exploit the best features of both.
List of approved abstract