Interests | Theory | Analysis | Gallery of Computations

Research Interests

Dynamical Systems Theory

My current research is focused on analysis and simulation of nonlinear dynamical systems. I consider myself as being on the borderline between applied mathematics and computer science. That means, I am interested in the development of numerical methods as well as the analysis of dynamical systems based on simulation and numerical computations. My research activities are targeted on 2D and 3D maps, but I also have some experience with ODEs.

Methods of Numerical Computation

The development of methods for the numerical investigation of dynamical systems is at the center of my research activities. Hereby, my interest covers all aspects of this field - the design and analysis of an approach in theory as well as the adaption and implementation for a practical application. The underlying technique for all approaches I implemented and/or designed is multilevel phase space discretization. The methods are aimed at the following investigation tasks:

Localization of periodic points
Localization of the chain recurrent set (contains all kinds of return trajectories)
Localization of attractors and repellers
Localization of the domain of attraction (lower and upper bound)
Computation of filtrations
Computation of (un)stable and connecting manifolds

The main advantage of the proposed methods is that they are applicable to a wide range of dynamical systems and do not require any a priori knowledge about the system.