For the case of generic 4d symplectic maps with a mixed phase space, we investigate the global organization of regular tori. For this, we compute elliptic 1-tori of two coupled standard maps and display them in a 3d phase-space slice. This visualizes how all regular 2-tori are organized around a skeleton of elliptic 1-tori in the 4d phase space. The 1-tori occur in two types of one-parameter families: (α) Lyapunov families emanating from elliptic-elliptic periodic orbits, which are observed to exist even far away from them and beyond major resonance gaps, and (β) families originating from rank-1 resonances. At resonance gaps of both types of families either (i) periodic orbits exist, similar to the Poincaré-Birkhoff theorem for 2d maps, or (ii) the family may form large bends. In combination, these results allow for describing the hierarchical structure of regular tori in the 4d phase space analogously to the islands-around-islands hierarchy in 2d maps.

pre-print version appears in Int. J. Mod. Phys. B 27 (2013) 1230001 First experiments on the growth of oxypnictide F-doped LaFeAsO thin films indicated an incomplete normal-to-superconducting transition and offered a work programme challenging to overcome possible difficulties in their fabrication. In this regard the possibility of an all in-situ epitaxial growth appeared to be a matter of time and growth parameters. The following review clarifies that F-doped oxypnictide thin films are extremely difficult to grow by in-situ PLD due to the formation of very stable impurity phases such as oxyfluorides (LaOF) and oxides (La 2 O 3 ) and the loss of stoichiometry possibly due to incongruent evaporation of the target or re-evaporation of volatile elements at the substrate surface. However, the review also demonstrates that the employed twostep fabrication process for oxypnictide thin films has been successfully applied in the preparation of clean polycrystalline as well as of epitaxial thin films. Fundamental investigations on the upper critical field, its temperature dependence and its anisotropy contributed to an understanding of multiband superconductivity in oxypnictides.

The regular structures of a generic 4d symplectic map with a mixed phase space are organized by one-parameter families of elliptic 1d-tori. Such families show prominent bends, gaps, and new branches. We explain these features in terms of bifurcations of the families when crossing a resonance. For these bifurcations, no external parameter has to be varied. Instead, the longitudinal frequency, which varies along the family, plays the role of the bifurcation parameter. As an example, we study two coupled standard maps by visualizing the elliptic and hyperbolic 1d-tori in a 3d phase-space slice, local 2d projections, and frequency space. The observed bifurcations are consistent with the analytical predictions previously obtained for quasi-periodically forced oscillators. Moreover, the new families emerging from such a bifurcation form the skeleton of the corresponding resonance channel.