@unpublished{FeudelSeehaferGalantietal.1996,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@unpublished{SeehaferZienickeFeudel1996,
  author    = {Seehafer, Norbert and Zienicke, Egbert and Feudel, Fred},
  title     = {Absence of magnetohydrodynamic activity in the voltage-driven sheet pinch},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14328},
  year      = {1996},
  abstract  = {We have numerically studied the bifurcation properties of a sheet pinch with impenetrable stress-free boundaries. An incompressible, electrically conducting fluid with spatially and temporally uniform kinematic viscosity and magnetic diffusivity is confined between planes at x1=0 and 1. Periodic boundary conditions are assumed in the x2 and x3 directions and the magnetofluid is driven by an electric field in the x3 direction, prescribed on the boundary planes. There is a stationary basic state with the fluid at rest and a uniform current J=(0,0,J3). Surprisingly, this basic state proves to be stable and apparently to be the only time-asymptotic state, no matter how strong the applied electric field and irrespective of the other control parameters of the system, namely, the magnetic Prandtl number, the spatial periods L2 and L3 in the x2 and x3 directions, and the mean values B¯2 and B¯3 of the magnetic-field components in these directions.},
  language  = {en}
}
@unpublished{ThiessenhusenEspositoKurthsetal.1995,
  author    = {Thiessenhusen, Kai-Uwe and Esposito, Larry W. and Kurths, J{\"u}rgen and Spahn, Frank},
  title     = {Detection of hidden resonances in Saturn's B-ring},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-13618},
  year      = {1995},
  abstract  = {The Voyager 2 Photopolarimeter experiment has yielded the highest resolved data of Saturn's rings, exhibiting a wide variety of features. The B-ring region between 105000 km and 110000 km distance from Saturn has been investigated. It has a high matter density and contains no significance features visible by eye. Analysis with statistical methods has let us to the detection of two significant events. These features are correlated with the inner 3:2 resonances of the F-ring shepherd satellites Pandora and Prometheus, and may be evidence of large ring paricles caught in the corotation resonances.},
  language  = {en}
}
@unpublished{Schmidtmann1995,
  author    = {Schmidtmann, Olaf},
  title     = {Modelling of the interaction of lower and higher modes in two-dimensional MHD-equations},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-13790},
  year      = {1995},
  abstract  = {The present paper is related to the problem of approximating the exact solution to the magnetohydrodynamic equations (MHD). The behaviour of a viscous, incompressible and resistive fluid is exemined for a long period of time. Contents: 1 The magnetohydrodynamic equations 2 Notations and precise functional setting of the problem 3 Existence, uniqueness and regularity results 4 Statement and Proof of the main theorem 5 The approximate inertial manifold 6 Summary},
  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}
}
@unpublished{Jansen1995,
  author    = {Jansen, Wolfgang},
  title     = {CANDYS/QA : algorithms, programs, and user's manual},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-13920},
  year      = {1995},
  abstract  = {Contents: I. Algorithms 1. Theoretical Backround 2. Numerical Procedures 3. Graph Representation of the Solutions 4. Applications and Example II. Users' Manual 5. About the Program 6. The Course of a Qualitative Analysis 7. The Model Module 8. Input description 9. Output Description 10. Example 11. Graphics},
  language  = {en}
}
@unpublished{FeudelSeehaferSchmidtmann1995,
  author    = {Feudel, Fred and Seehafer, Norbert and Schmidtmann, Olaf},
  title     = {Bifurcation phenomena of the magnetofluid equations},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-13585},
  year      = {1995},
  abstract  = {We report on bifurcation studies for the incompressible magnetohydrodynamic equations in three space dimensions with periodic boundary conditions and a temporally constant external forcing. Fourier reprsentations of velocity, pressure and magnetic field have been used to transform the original partial differential equations into systems of ordinary differential equations (ODE), to which then special numerical methods for the qualitative analysis of systems of ODE have been applied, supplemented by the simulative calculation of solutions for selected initial conditions. In a part of the calculations, in order to reduce the number of modes to be retained, the concept of approximate inertial manifolds has been applied. For varying (incereasing from zero) strength of the imposed forcing, or varying Reynolds number, respectively, time-asymptotic states, notably stable stationary solutions, have been traced. A primary non-magnetic steady state loses, in a Hopf bifurcation, stability to a periodic state with a non-vanishing magnetic field, showing the appearance of a generic dynamo effect. From now on the magnetic field is present for all values of the forcing. The Hopf bifurcation is followed by furhter, symmetry-breaking, bifurcations, leading finally to chaos. We pay particular attention to kinetic and magnetic helicities. The dynamo effect is observed only if the forcing is chosen such that a mean kinetic helicity is generated; otherwise the magnetic field diffuses away, and the time-asymptotic states are non-magnetic, in accordance with traditional kinematic dynamo theory.},
  language  = {en}
}
@unpublished{FeudelSeehafer1995,
  author    = {Feudel, Fred and Seehafer, Norbert},
  title     = {Bifurcations and pattern formation in a 2D Navier-Stokes fluid},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-13907},
  year      = {1995},
  abstract  = {We report on bifurcation studies for the incompressible Navier-Stokes equations in two space dimensions with periodic boundary conditions and an external forcing of the Kolmogorov type. Fourier representations of velocity and pressure have been used to approximate the original partial differential equations by a finite-dimensional system of ordinary differential equations, which then has been studied by means of bifurcation-analysis techniques. A special route into chaos observed for increasing Reynolds number or strength of the imposed forcing is described. It includes several steady states, traveling waves, modulated traveling waves, periodic and torus solutions, as well as a period-doubling cascade for a torus solution. Lyapunov exponents and Kaplan-Yorke dimensions have been calculated to characterize the chaotic branch. While studying the dynamics of the system in Fourier space, we also have transformed solutions to real space and examined the relation between the different bifurcations in Fourier space and toplogical changes of the streamline portrait. In particular, the time-dependent solutions, such as, e.g., traveling waves, torus, and chaotic solutions, have been characterized by the associated fluid-particle motion (Lagrangian dynamics).},
  language  = {en}
}
@unpublished{FeudelSeehaferSchmidtmann1995,
  author    = {Feudel, Fred and Seehafer, Norbert and Schmidtmann, Olaf},
  title     = {Fluid helicity and dynamo bifurcations},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-13882},
  year      = {1995},
  abstract  = {The bifurcation behaviour of the 3D magnetohydrodynamic equations has been studied for external forcings of varying degree of helicity. With increasing strength of the forcing a primary non-magnetic steady state loses stability to a magnetic periodic state if the helicity exceeds a threshold value and to different non-magnetic states otherwise.},
  language  = {en}
}
@unpublished{PikovskijZaksFeudeletal.1995,
  author    = {Pikovskij, Arkadij and Zaks, Michael A. and Feudel, Ulrike and Kurths, J{\"u}rgen},
  title     = {Singular continuous spectra in dissipative dynamics},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-13787},
  year      = {1995},
  abstract  = {We demonstrate the occurrence of regimes with singular continuous (fractal) Fourier spectra in autonomous dissipative dynamical systems. The particular example in an ODE system at the accumulation points of bifurcation sequences associated to the creation of complicated homoclinic orbits. Two different machanisms responsible for the appearance of such spectra are proposed. In the first case when the geometry of the attractor is symbolically represented by the Thue-Morse sequence, both the continuous-time process and its descrete Poincar{\´e} map have singular power spectra. The other mechanism owes to the logarithmic divergence of the first return times near the saddle point; here the Poincar{\´e} map possesses the discrete spectrum, while the continuous-time process displays the singular one. A method is presented for computing the multifractal characteristics of the singular continuous spectra with the help of the usual Fourier analysis technique.},
  language  = {en}
}