Address:Institute for Analysis and Scientific Computing
Vienna University of Technology
Wiedner Hauptstraße 8-10
A-1040 Wien, Austria
Telephone: +43 - 1 - 58801 - 10179
Fax: +43 - 1 - 58801 - 11599
Email: ilona.gucwa@asc.tuwien.ac.at
Advisor: Peter Szmolyan
Research: dynamical systems, geometric singular perturbation theory, applications
I became a WK-member in October 2007.
I'm interested in dynamical systems and their application to the natural and technical sciences. Many physical problems, particularly in chemical and biological systems, show dynamics in different time scales. My current research is focused on the simplest model of an autocatalytic process. Since the resulting equations gain their special structure from the presence of differing time scales, geometric singular perturbation theory can be applied to describe the dynamics of the autocatalator.
Master thesis:
Title: Symplectic analysis of a Whitham - type nonlinear dynamical system and its integrability.
Supervisor: A. K. Prykarpatski, Ph.D., D.Sc., Professor; AGH University of Science and Technology, Cracow 2007.
My Master's Thesis is devoted to the investigation of the bi-hamiltonicity and complete integrability of a non-local Whitham- type dynamical system on infinite dimensional differentiable manifold. Based on the gradient type Lax equation ultimately related with our dynamical system, an infinite recurrent hierarchy of conserved dispersive functionals is constructed. Making use of some first smooth functional invariants with nontrivial dispersion, the finite dimensional reductions on the invariant subset of critical points of the corresponding Lagrangian functional is constructed via the classical Novikov-Bogoyavlensky approach. The related finite dimensional canonical Hamiltonian dynamical systems are constructed; their Liouville- Arnold integrability by quadratures is proved.