@unpublished{BraunFeudel1996,
  author    = {Braun, Robert and Feudel, Fred},
  title     = {Supertransient chaos in the two-dimensional complex Ginzburg-Landau equation},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14099},
  year      = {1996},
  abstract  = {We have shown that the two-dimensional complex Ginzburg-Landau equation exhibits supertransient chaos in a certain parameter range. Using numerical methods this behavior is found near the transition line separating frozen spiral solutions from turbulence. Supertransient chaos seems to be a common phenomenon in extended spatiotemporal systems. These supertransients are characterized by an average transient lifetime which depends exponentially on the size of the system and are due to an underlying nonattracting chaotic set.},
  language  = {en}
}
@unpublished{FeudelSeehaferGalantietal.1996,
  author    = {Feudel, Fred and Seehafer, Norbert and Galanti, Barak and R{\"u}diger, Sten},
  title     = {Symmetry breaking bifurcations for the magnetohydrodynamic equations with helical forcing},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14317},
  year      = {1996},
  abstract  = {We have studied the bifurcations in a three-dimensional incompressible magnetofluid with periodic boundary conditions and an external forcing of the Arnold-Beltrami-Childress (ABC) type. Bifurcation-analysis techniques have been applied to explore the qualitative behavior of solution branches. Due to the symmetry of the forcing, the equations are equivariant with respect to a group of transformations isomorphic to the octahedral group, and we have paid special attention to symmetry-breaking effects. As the Reynolds number is increased, the primary nonmagnetic steady state, the ABC flow, loses its stability to a periodic magnetic state, showing the appearance of a generic dynamo effect; the critical value of the Reynolds number for the instability of the ABC flow is decreased compared to the purely hydrodynamic case. The bifurcating magnetic branch in turn is subject to secondary, symmetry-breaking bifurcations. We have traced periodic and quasi- periodic branches until they end up in chaotic states. In particular detail we have analyzed the subgroup symmetries of the bifurcating periodic branches, which are closely related to the spatial structure of the magnetic field.},
  language  = {en}
}
@unpublished{EngbertScheffczykKrampeetal.1997,
  author    = {Engbert, Ralf and Scheffczyk, Christian and Krampe, Ralf-Thomas and Rosenblum, Mikhael and Kurths, J{\"u}rgen and Kliegl, Reinhold},
  title     = {Tempo-induced transitions in polyrhythmic hand movements},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14380},
  year      = {1997},
  abstract  = {We investigate the cognitive control in polyrhythmic hand movements as a model paradigm for bimanual coordination. Using a symbolic coding of the recorded time series, we demonstrate the existence of qualitative transitions induced by experimental manipulation of the tempo. A nonlinear model with delayed feedback control is proposed, which accounts for these dynamical transitions in terms of bifurcations resulting from variation of the external control parameter. Furthermore, it is shown that transitions can also be observed due to fluctuations in the timing control level. We conclude that the complexity of coordinated bimanual movements results from interactions between nonlinear control mechanisms with delayed feedback and stochastic timing components.},
  language  = {en}
}
@unpublished{BraunFeudelGuzdar1998,
  author    = {Braun, Robert and Feudel, Fred and Guzdar, Parvez},
  title     = {The route to chaos for a two-dimensional externally driven flow},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14717},
  year      = {1998},
  abstract  = {We have numerically studied the bifurcations and transition to chaos in a two-dimensional fluid for varying values of the Reynolds number. These investigations have been motivated by experiments in fluids, where an array of vortices was driven by an electromotive force. In these experiments, successive changes leading to a complex motion of the vortices, due to increased forcing, have been explored [Tabeling, Perrin, and Fauve, J. Fluid Mech. 213, 511 (1990)]. We model this experiment by means of two-dimensional Navier-Stokes equations with a special external forcing, driving a linear chain of eight counter-rotating vortices, imposing stress-free boundary conditions in the vertical direction and periodic boundary conditions in the horizontal direction. As the strength of the forcing or the Reynolds number is raised, the original stationary vortex array becomes unstable and a complex sequence of bifurcations is observed. Several steady states and periodic branches and a period doubling cascade appear on the route to chaos. For increasing values of the Reynolds number, shear flow develops, for which the spatial scale is large compared to the scale of the forcing. Furthermore, we have investigated the influence of the aspect ratio of the container as well as the effect of no-slip boundary conditions at the top and bottom, on the bifurcation scenario.},
  language  = {en}
}
@unpublished{MaassRieder1996,
  author    = {Maaß, Peter and Rieder, Andreas},
  title     = {Wavelet-accelerated Tikhonov-Phillips regularization with applications},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14104},
  year      = {1996},
  abstract  = {Contents: 1 Introduction 1.1 Tikhanov-Phillips Regularization of Ill-Posed Problems 1.2 A Compact Course to Wavelets 2 A Multilevel Iteration for Tikhonov-Phillips Regularization 2.1 Multilevel Splitting 2.2 The Multilevel Iteration 2.3 Multilevel Approach to Cone Beam Reconstuction 3 The use of approximating operators 3.1 Computing approximating families {Ah}},
  language  = {en}
}
@unpublished{DickenMaass1995,
  author    = {Dicken, Volker and Maaß, Peter},
  title     = {Wavelet-Galerkin methods for ill-posed problems},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-13890},
  year      = {1995},
  abstract  = {Projection methods based on wavelet functions combine optimal convergence rates with algorithmic efficiency. The proofs in this paper utilize the approximation properties of wavelets and results from the general theory of regularization methods. Moreover, adaptive strategies can be incorporated still leading to optimal convergence rates for the resulting algorithms. The so-called wavelet-vaguelette decompositions enable the realization of especially fast algorithms for certain operators.},
  language  = {en}
}