Final Report Summary - BREUDS (Brazilian-European partnership in Dynamical Systems)
In recent years and decades important progress has been made to understand the (generic) dynamics of low- dimensional (intrinsically autonomous, i.e. time-independent) dynamical systems, leading to the identification of new challenges, including high-dimensional dynamical systems (including PDEs and other types of functional differential equations), dynamical systems with particular structure (such as Hamiltonian systems, systems with symmetry, and systems on networks), and intrinsically nonautonomous dynamical systems (including dynamical systems with random elements).
This joint research programme between Europe and Brazil relies on strong traditions in dynamical systems at both ends, and complementary expertise that will drive innovation and resolve open problems at the forefront of modern dynamical systems research. Typically for the multifaceted field of dynamical systems, the identified work packages have many places of contact among each other, and thus naturally form part of one scientific community, inspiring and challenging each other in many ways.
During the existence of this IRSES project, excellent progress has been made in the research projected for each of the five main Work Packages, concerning non-autonomous dynamical systems, ergodic theory, low-dimensional dynamics, Hamiltonian dynamics and bifurcation theory, in terms of their objectives, tasks, deliverables and milestones. BREUDS has supported internationally leading research in all these directions, as well a number of workshops and conferences were dissemination, transfer of knowledge and training has taken place.
Research collaborations have already led to many publications in international peer reviewed journals. It also supported the work of many ESRs doing their PhD research.
BREUDS has celebrated the 2014 Fields medal laureats Prof Martin Hairer (Warwick) and Prof Artur Avila (IMPA, CNRS) who are directly involved with and beneficiaries of this IRSES.
For more information on BREUDS, please see the project website at (http://www.ma.ic.ac.uk/DynamIC/BREUDS).