Colloquium Mathematics, Prof.dr. Henk W. Broer

Join us for coffee and tea at 15.45 p.m.

 

Date: Tuesday, February 22^nd 2011

Speaker: Prof.dr. Henk Broer

Room: 5161.0267 (Bernoulliborg),

Time: 16.15

 

 

Title:Resonance and fractal geometry.


Abstract:  

The lecture concerns a number of resonance phenomena and the
mathematical theory behind this in terms of parameter dependent
dynamical systems. I will deal with two concrete cases, of which one
goes back to Christiaan Huygens and the other is related to the
Botafumeiro in Santiago de Compostela. In relation to this a number of
`universal' problems will be discussed, related to Hopf bifurcations in
a general sense. It turns out that resonance in the parameter space is
organized by `tongues', the precise forms of which can be revealed by
Singularity Theory.  Here the corresponding resonant dynamics is mainly
periodic. In between the tongues there is a fractal set that is built
from a Cantor set of positive measure, where the corresponding dynamics
is mainly multi-periodic.  In the overall transitions also chaotic
dynamics may occur.

 

Colloquium coordinators are Prof.dr. A.C.D. van Enter (e-mail : A.C.D.van.Enter@rug.nl) and

Dr. M. Dür (e-mail: M.E.Dur@rug.nl)