Lorenz Strange Atractors
 
 
Description:  The Lorenz strange attractor, introduced in the sixties in the context of thermal convection and weather prediction, became a paradigm chaotic behavior, and a crucial model to try and describe this type of dynamics.

In the nineties there were two fundamental developments:

On the one hand, three and a half decades after Lorenz' original paper, W. Tucker, then a graduate student at KTH-Stockholm, was able to prove that the Lorenz equations do exhibit some strange attractor. His proof combines a careful analysis of the equations near the equilibrium point with rigorous computations.

On the other hand, a mathematical theory of chaotic behavior for three-dimensional vector fields was built, that encompasses the phenomenon of robust accumulation of equilibrium points by recurrent regular orbits. The main result, due to C. Morales, M. J. Pacifico, and E. Pujals, states that any robust invariant ser that contains an equilibrium must be a Lorenz-like attractor!

Currently, much effort is being devoted to extending this theory to higher dimensions (arbitrary number of degrees of freedom).


Marcelo Viana is a Professor of Mathematics and Deputy Director of the Institute of Pure and Applied Mathematics (IMPA), Rio de Janeiro, Brazil. Born in Rio de Janeiro on March 4, 1962, of Portuguese parents, he was educated in Portugal, for where he came at only the age of three months. He received his B.S. from the University of Porto in 1984, where he held a position, and got his Ph.D. from the IMPA in 1990, with a thesis entitled "Strange attractors in higher dimensions", written under the direction of Jacob Palis. He was awarded a Guggenheim fellowship to work at UCLA and Princeton in 1993, and since then he has been a visitor to main centers around the world. Marcelo Viana is a well-known mathematician worldwide in the fields of dynamical systems where he has made important contributions. His research focuses on dynamical systems, ergodic theory, and bifurcation theory. He has published more than 50 research articles in international journals (including Acta Mathematica, Annals of Mathematics, Inventiones Mathematicae and Publications Mathématiques de l'IHES) and has already supervised seventeen Ph.D. thesis. Marcelo Viana has both Portuguese and Brazilian nationalities. Although he works in Brazil, he keeps strong links with mathematics in Portugal, by participating in research evaluation panels, conferences and seminars, and by supervising several Portuguese Ph.D. students. He is also a member of the Scientific Council of CIM. Invited to give talks at two consecutive International Congresses of Mathematicians, Zurich-94 and Berlin-98 (the former as Section Speaker and the latter as Plenary Lecturer) he is considered a superb lecturer. Besides, he was also invited to give a Plenary Lecture at the International Congress on Mathematical Physics (Paris, 1994). He is on the editorial board of seven mathematical journals: Ergodic Theory & Dynamical Systems, Dynamical Systems: An International Journal, Portugaliae Mathematica, Discrete and Continuous Dynamical Systems, Journal of Stochastics and Dynamics, Nonlinear Differential Equations and Applications, Dynamics of Partial Differential Equations. Among his several prizes and distinctions are The Mathematical Union for Latin America and the Caribbean Award in Mathematics, 2000, the Great Cross of Scientific Merit, granted by the President of Brazil in 2000, Member of the Third World Academy of Sciences (elected in 2000), Third World Academy of Sciences Award in Mathematics, 1998, Member of the Brazilian Academy of Sciences (elected in 1997). Last December Marcelo Viana was the first recipient of the Ramanujan Prize, which honors a researcher, younger than 45 years old, who has conducted outstanding research in a developing country. The prize is funded by the Niels Henrik Abel Memorial Fund and it is awarded by the Abdus Salam International Centre for Theoretical Physics in conjunction with the International Mathematical Union.
Area(s):

Start Date:  2006-02-14
Start Time:   15:00
Speaker:  Marcelo Viana (IMPA, Brasil)
Place:  Sala 2.4 - Departamento de Matemática
See more:   <Main>  
 
© Centre for Mathematics, University of Coimbra, funded by
Science and Technology Foundation
Powered by: rdOnWeb v1.4 | technical support