Heinz Hanßmann

Mathematisch Instituut

Universiteit Utrecht

Postbus 80.010

3508 TA Utrecht

The Netherlands

email :
Heinz.Hanssmann@math.uu.nl

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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).