Colloquium Mathematics, Prof.dr. Henk W. Broer
Join us for coffee and tea at 15.45 p.m.
Date: Tuesday, February 22nd 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)
| Last modified: | 10 February 2021 2.29 p.m. |
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