Permanent Faculty
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Morten Brøns, Professor, Head of section
Keywords: dynamical systems, mathematical modelling, vortex dynamics, singular perturbations, model reduction, mathematical chemistry, mathematical biology, fluid mechanics, non-linear vibrations, bifurcation theory
I work with various aspects of dynamical systems that can be modelled by non-linear differential equations, mostly ordinary differential equations. The applications span from biology and chemistry to fluid and solid mechanics. My research is currently focused on two topics: 1) Singular perturbation (or slow-fast) systems with several time scales. This includes efficient model reduction methods, where one tries to eliminate the short-term fast dynamics and mixed-mode oscillations where a limit cycle changes between small and large amplitude behavior. 2) Bifurcation theory for vortices: Developing mathematical descriptions of vortex structures in fluid flows with the special purpose of understanding the creation, interaction and merging of vortices. read more
Kristian Uldall Kristiansen, Associate ProfessorKeywords: dynamical systems, differential equations, invariant manifolds, geometric singular perturbation theory, the blowup method, piecewise smooth systems
My research is focused on global analysis of (low dimensional) dynamics in ordinary differential equations. In my research articles, I frequently prove existence (and uniquness/bifurcations/etc.) of limit cycles - occasionally in models coming from applications (mechanics/biology/chemistry/etc.) - using Geometric Singular Perturbation Theory (GSPT), with the blowup method as the key technical tool. This theory is relevant for the solution of Hilbert's 16 problem (on the number of limit cycles in planar polynomial systems), but my main contribution to the field has been the extension of GSPT to (a) systems with non-polynomial growth and (b) systems close to piecewise smooth ones. Future directions of my research include GSPT with complex time, with the aim to "merge" oscillatory dynamics, a previous focus area of my research, with hyperbolic dynamics. read more
Christian Henriksen, Associate ProfessorKeywords: Dynamical systems, Industrial Mathematics, Complex Analysis, Potential Theory, Holomorphic Dynamics
I'm broadly interested in mathematics and how to apply it to real world problems. On a more pure level, I'm interested in the dynamics of holomorphic mappings, such as those of extremal polynomials. The techniques I use, come from the theory of quasiconformal maps and deformations, holomorphic motions and potential analysis. read more
PhDs, Postdocs and Research Assistants
Coming soon.