Address:Institut for Applied Mathematics and Numerical Analysis
Vienna University of Technology
Wiedner Hauptstraße 8-10
A-1040 Wien, Austria
Telephone: (++43)(1) 58801-11537
Fax: (++43)(1) 58801-11599
Email: Astrid.Huber@tuwien.ac.at
Advisor: Peter Szmolyan
Research: Generally I'm interested in dynamical systems and mathematical applications to problems in biology and technology.
My main aerea in dynamical sytems are singularly perturbed equations, which show dynamics on different timescales. I'm trying to apply geometric theories, especially Fenichel's singular perturbation theory to describe their qualitative behaviour. Since most of these theories only work for regular points, I'm using the blow up transformation to extend these methods to singular points.
In my matster thesis I worked on the Takens Bogdanov equation with
slowly varying parameters.
The theme of my thesis is slow-fast dynamics in laser
equations. Since most lasers show dynamics on different timescales
it is possible to apply geometric singular perturbation
theory to describe a part of their behaviour. Mainly I'm working on a
laser with a saturable
absorber,
which is described by the Yamada Model. One of the interesing
features of this laser is that the laser beam can show
high frequency oscillations, which correspond to periodic orbits of
the laser equations.