Heinz Hanßmann

Mathematisch Instituut
Universiteit Utrecht
Postbus 80.010
3508 TA Utrecht
The Netherlands

email : Heinz.Hanssmann@math.uu.nl

Research interests : dynamical systems, in particular Hamiltonian systems

Dynamical systems

This branch of mathematics deals with the evolution of systems. They can be based on models from inside or outside of mathematics. Typical examples come from physics (celestial mechanics, resonant circuit), chemistry (reaction-diffusion equations) biology (predator-prey systems) or economy (market models) -- this short list is far from exhaustive. In mathematical terms they often can be described by an ordinary differential equation x'=f(x).

When differential equations were invented one used to (try to) find single solutions to given initial conditions. Nowadays one is increasingly interested in the global properties of the system: What are the relations between the solutions ? Are there classes of solutions with special properties ? It is a question of major interest, whether small perturbations have little influence on the global dynamics of the system or cause dramatic changes (structural stability, bifurcation).

Hamiltonian systems

My own research has been mostly in Hamiltonian systems. This is a special class of dynamical systems that was designed to describe idealised mechanical or astronomical motions, in particular the preservation of energy is `built into the theory' (there is no friction).

It is possible to roughly divide the subject of my papers into three groups, so click on rigid body, resonant oscillators or bifurcations for more details. Inevitably, papers of one group may use examples or results from another group, and you may find a list of all my available preprints up to 2004 in the README file of my ftp directory. For preprints from 2005 onwards see the list of Preprints of the Department of Mathematics. Alternatively, you can browse through MathSciNet or the MATH database (if you have access to these).