Chaotic Maps, Control Parameter, and Liapunov Exponent

We describe a one-dimensional chaotic map wherethe Liapunov exponent is a smooth function of a controlparameter.     

The generator coordinate approximation for molecules: A review

The generator coordinate approximation is a non-adiabatic theory of molecular systems. Its fundamental outlines were developed during the 1970's. A further analysis and first applications were published during the 1980's. In this paper, we review the present status of the theory.     

Algebraic cycles and topology of real Enriques surfaces

For a real Enriques surface Y we prove that every homology class in H₁(Y (R), Z/2) can be represented by a real algebraic curve if and only if all connected components of Y(R) are orientable. Furthermore, we give a characterization of real Enriques surfaces which are Galois-Maximal and/or Z-Galois-Maximal and we determine the Brauer group of any real Enriques surface Y.     

Strain analysis of Si by FEM and energy-filtering CBED.

Lattice strains around a platelet oxygen precipitate in Si wafer is studied by energy filtering convergent-beam electron diffraction (CBED) and calculations based on the finite element method (FEM). Local lattice strains are measured from CBD patterns obtained with a probe size less than 2 nm in a specimen thicker than 450 nm. Strains measured are compressive along a direction normal to a plate of the precipitation and tensile along a direction parallel to the plate. Two-dimensional stress fields near the precipitate are obtained with FEM computer analyses by fitting the measured strains. It appears that shear stresses are concentrated at the end of the precipitate edge and the maximum shear stress at an interface between the precipitate and the Si-matrix is 1.9 GPa. It is demonstrated that a combination of the energy filtering CBED and FEM is very useful for the study of local strains near interfaces in semiconductor devices, in particular for the study of stress fields that are too steep for application of the conventional CBED technique.     

Γ-type-invariants associated toPU(2)-bundles and the differentiable structure of Barlow's surface

Supported by a Heisenberg-scholarship of the DFG     

Maximal Lyapunov exponent and rotation numbers for two coupled oscillators driven by real noise

Asymptotic expansions for the exponential growth rate, known as the Lyapunov exponent, and rotation numbers for two coupled oscillators driven by real noise are constructed. Such systems arise naturally in the investigation of the stability of steady-state motions of nonlinear dynamical systems and in parametrically excited linear mechanical systems. Almost-sure stability or instability of dynamical systems depends on the sign of the maximal Lyapunov exponent. Stability conditions are obtained under various assumptions on the infinitesimal generator associated with real noise provided that the natural frequencies are noncommensurable. The results presented here for the case of the infinitesimal generator having a simple zero eigenvalue agree with recent results obtained by stochastic averaging, where approximate ItÔ equations in amplitudes and phases are obtained in the sense of weak convergence.Dedicated to Thomas K. Caughey on the occasion of his 65th birthday.