MathKoll. am 15.02./Prof. Warwick Tucker

[Institut für Mathematik]

Mathematisches Kolloquium

EINLADUNG

zu einem

VORTRAG

von

Prof. Dr. Warwick Tucker
(Dept. of Math., Uppsala University, Sweden)

mit dem Thema:

''The Lorenz attractor exists''

Abstract:
Four decades ago, the meteorologist Edward Lorenz introduced a simplified
model of atmospheric dynamics in his now famous article "Deterministic
Non-periodic Flow" published in the Journal of Atmospheric Sciences. The
simple system of differential equations produced amazingly complicated
solutions. One stunning property was that solutions starting very close
together were separated at an exponential rate. This gave rise to the
concept of the "butterfly effect", and seriously undermined the idea of a
deterministic world. Another feature of the system was that almost all
solutions tended to an invariant set on which they moved in a non-periodic
fashion.

For over 35 years Lorenz' equations defied all attempts at proving that they
really exhibit a so called "strange attractor". In this talk, I will present
a proof of this fact, produced during my graduate studies at Uppsala
University. By using a combination of pure and applied mathematics, it is
possible to prove that the equations do indeed give rise to a strange
attractor. Moreover, the attractor is robust, i.e., all nearby systems will
display similar strange attractors. The proof has two main ingredients:
rigorous numerics - which produces information about the global behaviour of
the system, and normal form theory - which deals with subtle local
properties of the solutions.

This work was described in Nature (by Ian Stewart), and won several prizes,
e.g. the European Mathematical Society Prize, and the R. E. Moore Prize for
Applications of Interval Analysis.

Zeit: Mittwoch, 15. Februar 2006,
         15.45 Uhr (Kaffeejause), anschlieszend 16.15 Uhr Vortrag

Ort: Fakultaet fuer Mathematik der Universitaet Wien, Nordbergstr. 15,
       Seminarraum C 2.09

Harald Rindler
Arnold Neumaier