Analysis
Our analysis research has three branches
Applied Analysis
The applied analysis subprogram covers theoretical analysis of parameter-dependent dynamical systems generated by various types of differential and difference equations, applications of dynamical systems theory to research problems, and the development of numerical methods and computer tools for the analysis of dynamical systems.
The goal of the subprogram is to apply the dynamical systems theory to study the nonlinear evolution of natural and artificial systems. This often requires new insights leading to the development of new dynamical systems theory, as well as new numerical methods and computer software. We study dynamical systems in finite and infinite dimensional spaces and their bifurcations.
Pure Analysis
The general mission of the pure analysis programme is to advance the deeper understanding of phenomena of analysis. This is often most fruitful in specific situations arising from geometry, symmetry, dynamical systems, and applications.
Research themes that have been pursued within the programme are Lie groups and symmetric spaces, their harmonic analysis and associated representation theory; connections with partial differential equations and distributions (
van den Ban).
Another line of research has been the investigation of dynamical systems, in particular Hamiltonian ones; reduction of these systems through symmetries; stability of approximate symmetries, bifurcations (
Hanßmann).
Bruggeman investigates analytic aspects of the theory of automorphic forms.