@unpublished{BraunFeudel1996, author = {Braun, Robert and Feudel, Fred}, title = {Supertransient chaos in the two-dimensional complex Ginzburg-Landau equation}, url =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} } @book{BraunFeudel1996, author = {Braun, Robert and Feudel, Fred}, title = {Supertransient chaos in the two-dimensional complex Ginzburg-Landau equation}, series = {Preprint NLD}, volume = {29}, journal = {Preprint NLD}, publisher = {Univ.}, address = {Potsdam}, pages = {8 S.}, year = {1996}, language = {en} } @unpublished{FeudelSeehaferGalantietal.1996, author = {Feudel, Fred and Seehafer, Norbert and Galanti, Barak and R{\"u}diger, Sten}, title = {Symmetry breaking bifurcations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} } @article{FeudelSeehaferRuediger1996, author = {Feudel, Fred and Seehafer, Norbert and R{\"u}diger, Sten}, title = {Symmetry breaking bifurcations for the magnetohydrodynamic equations with helical forcing}, series = {Preprint NLD}, volume = {31}, journal = {Preprint NLD}, publisher = {Univ.}, address = {Potsdam}, pages = {10 S.}, year = {1996}, language = {en} } @unpublished{Feudel1996, author = {Feudel, Ulrike}, title = {Komplexes Verhalten in multistabilen, schwach dissipativen Systemen}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14412}, year = {1996}, abstract = {Anhand eines paradigmatischen Modellbeispiels werden die Konsequenzen der Koexistenz vieler Attraktoren auf die globale Dynamik schwach dissipativer Systeme studiert. Es wird gezeigt, dass diese Systeme eine sehr reichhaltige Dynamik besitzen und extrem sensitiv gegen{\"u}ber St{\"o}rungen in den Anfangsbedingungen sind. Diese Systeme zeichnen sich durch eine extrem hohe Flexibilit{\"a}t ihres Verhaltens aus.}, language = {de} } @book{Feudel1996, author = {Feudel, Ulrike}, title = {Komplexes Verhalten in multistabilen, schwach dissipativen Systemen}, series = {Preprint NLD}, volume = {34}, journal = {Preprint NLD}, publisher = {Univ.}, address = {Potsdam}, pages = {11 S.}, year = {1996}, language = {de} } @unpublished{Jansen1996, author = {Jansen, Wolfgang}, title = {A note on the determination of the type of communication areas}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14339}, year = {1996}, abstract = {The paper presents a method that determines, by standard numerical means, the type of mutual relations of fold and flip bifurcations (configured as a so-called communication area) of a map. Equation systems are developed for the computation of points where a transition between areas of different types occurs. Furthermore, it is shown that saddle area<->spring area transitions can exist which have not yet been considered in the literature. Analytical conditions of that transition are derived.}, language = {en} } @book{Jansen1996, author = {Jansen, Wolfgang}, title = {A note on the determination of the type of communication areas}, series = {Preprint NLD}, volume = {33}, journal = {Preprint NLD}, publisher = {Univ.}, address = {Potsdam}, pages = {32 S.}, year = {1996}, 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} } @book{MaassRieder1996, author = {Maaß, Peter and Rieder, Andreas}, title = {Wavelet-accelerated Tikhonov-Phillips regularization with applications}, series = {Preprint NLD}, volume = {30}, journal = {Preprint NLD}, publisher = {Univ.}, address = {Potsdam}, pages = {25 S.}, year = {1996}, language = {en} }