Dynamical Systems

The area of Dynamical Systems has its beginning at the University of Porto in 1982 when José Basto-Gonçalves returned to the former Department of Applied Mathematics at the Faculty of Sciences, having obtained his PhD at the University of Warwick working on Hamiltonian systems. A year later, Isabel Labouriau was hired by the same department after obtaining her PhD at the University of Warwick under the guidance of Ian Stewart. I. Labouriau and J. Basto-Gonçalves started a research line on Geometrical Methods on Differential Equations. In the 90s, Sofia Castro and Ana Paula Dias joined this research line, both after obtaining their PhDs at the University of Warwick also under the guidance of Ian Stewart. In the 2000s, Manuela Aguiar, Carla Pinto, Célia Moreira, Alexandre Rodrigues and Helena Reis also joined this research line, all of them after obtaining the PhD at the University of Porto under the supervision or co-supervision of members of CMUP. In the scientific production of some of the aforementioned members of this line it is possible to detect a strong component of research in Singularity Theory. In turn, Helena Reis has devoted substantial part of her work to the study the dynamics of holomorphic foliations and their singularities.

A distinct component in the area of Dynamical Systems has its beginning in the early 90s, after some members of the former Department of Pure Mathematics of the Faculty of Sciences have obtained their PhD degree at IMPA, mainly through the influence of M. Arala Chaves (now retired), firstly Maria Carvalho, Jorge Rocha and Marcelo Viana (a former member of CMUP for a couple of years) and later José Ferreira Alves. Maria Carvalho, under the guidance of Ricardo Mañé, Jorge Rocha and Marcelo Viana under the guidance of Jacob Palis and José Ferreira Alves under the guidance of Marcelo Viana (who in the meantime was hired by IMPA). While Jorge Rocha has his work mostly in Stability and Bifurcation of Dynamical Systems, the others opened a new line of research in Ergodic Theory, particularly interested in the study of chaotic dynamical systems from a probabilistic perspective. In the 2000s, Ana Cristina Freitas and Jorge Freitas joined this research line, both after getting their PhD at the University of Porto, the latter under the guidance of Maria Carvalho and José Ferreira Alves. With a solid background in Probability Theory, Ana Cristina Freitas and Jorge Freitas opened a more specific line of research in Extreme Value Theory for chaotic dynamics.

These two components were initially at separate research centres. Interaction has increased when the centres were merged in 2002 and a weekly Dynamical Systems seminar was established. This line has currently 13 members, 11 of whom are permanent.

The theory of Dynamical Systems is the confluence of knowledge in several areas of Mathematics. We can easily detect among the members of this line of CMUP basic training with components in Algebra, Analysis, Geometry, Probability Theory and Topology. If, on the one hand, the members representing this line of research are scattered through all the research groups of CMUP according to the organization in four classical areas of Mathematics, it should also be enhanced that they demonstrate ability for internal communication and interaction, as evidenced by the weekly Seminar on Dynamical Systems that remains active for almost a decade. It is precisely in this confluence of knowledge in several areas, with the major common goal of understanding the behaviour of systems described by iterative processes, that lies the richness of this thematic line, greatly contributing to an ambience of interaction among the various research groups of CMUP.
 

Principal investigator

Integrated members

Associated members

Temporary members - phd students