Dynamics of Structured Systems

By Oliver Junge
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Mathematisches Forschungsinstitut Oberwolfach

Dynamics of Structured Systems

December 14-20, 2003
Mathematisches Forschungsinstitut Oberwolfach, Germany
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.

Dynamics of Structured Systems, group photo, December 2003
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:

  1. "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).
  2. "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

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