Organized by |
Wolf-Jürgen
Beyn (Universität Bielefeld), |
Bernold Fiedler (Freie Universität, Berlin)
and |
John Guckenheimer (Cornell
University) |
The main purpose of the conference was to present and discuss
current progress in the mathematical analysis as well as in numerical
methods for dynamical systems that show special structures. Among the
topics treated were:
- different time scales, in particular singularly perturbed
systems,
- invariant manifolds and dimension reduction,
- symmetries or Hamiltonian structures of the underlying vector
field,
- spatio-temporal phenomena in time-dependent partial differential
equations, such as shock waves, fronts and spiral waves,
- synchronized and desynchronized behavior of coupled oscillator
chains,
- statistical analysis of longtime behavior.
The various sessions were organized in such a way that each of the
topics was discussed from an analytical and a numerical point of
view. Several new approaches were presented and new areas of
applications appeared, mainly to biological and physical systems.
Many of the presentations revealed that, in spite of substantial
progress over the last years, our mathematical understanding of the
additional structures in dynamical systems has to be deepened further
in order to fully grasp their influence on asymptotic behavior and to
exploit far-reaching applications to real-world problems. For such an
achievement further joint efforts by mathematicians working in the
areas of theory, numerics and applications of dynamical systems are
desirable.
|
Group photo taken at the workshop Dynamics
of Structured Systems in December
2003. |
A total of 34 talks were presented by leading experts in the field;
see also the
complete
list of abstracts. On one afternoon two parallel problem sessions
were held:
- "Multiscale Dynamics", organized by Klaus Schneider (WIAS, Berlin)
Issues under considerations were: Singularly perturbed
differential-delay equations (Hadeler, Mallet-Paret, Schneider),
approaches in case of loss of hyperbolicity (Szmolyan, Schneider),
biological applications (Doedel, Hadeler), open problems in continuum
mechanics (Mielke).
- "Rigorous numerics and numerical dynamics", organized by Lars
Grüne (Bayreuth) and Oliver Junge (Paderborn)
The issues were related to the question 'how false conclusions from
numerical computations about the dynamics of the underlying dynamical
system can be avoided'. In particular the discussion focused on
high-dimensional systems and on methods that use the Conley
index.
© 2003 Mathematisches Forschungsinstitut
Oberwolfach
Provided by Oliver Junge, Universität Paderborn, Germany