Numerical evidence is presented that perturbations away from analyticity change the qualitative structure of the Mandelbrot set. The changes affect both the form and the surface structure. Most characteristically, the infinitely thin “necks” disappear. At at least one place, the surface structure becomes smooth.
A variety of surprising effects arise from the nonlinear light-matter interaction of circularly polarized laser light propagating through sodium vapor. We present experimental evidence for an asymmetry in the absorption of left hand and right hand circularly polarized light as well as for the creation of a collimated light beam of apposite polarization within the light-matter interaction region. Both effects are not yet explained by common theories.
Nonlinear current transport behavior during low-temperature avalanche breakdown of germanium comprises the spontaneous formation of spatial and temporal dissipative structures in the formerly homogeneous semiconductor. Due to the simultaneous presence of two and more competing fundamental oscillatory modes intrinsic to our synergetic semiconductor system, selforganized emergence of quasiperiodic and mode-locked states can be observed followed by the quasiperiodic approach to low-dimensional chaos.
The generalized Mandelbrot set, described previously, contains - like the original Mandelbrot set - non-differentiable self-similar fractal structures. An example looking like a vortex structure is presented along with a corresponding generalized Julia set.
This paper gives a concrete physical interpretation of a simple dynamical model based on the universal Rashevsky- Turing theory of symmetry-breaking morphogenesis in terms of spatio-temporal nonlinear transport phenomena in a synergetic semiconductor system.
Generalized Mandelbrot sets arise in perturbed (non-analytic) versions of the complex logistic map. Numerically, it contains smooth portions as shown previously. To exclude that this result is specific to particular initial conditions only, the structure of the analogue to the Fatou set is looked at in the region in question. The set of non-divergent points is being "eaten up" by a smooth invading boundary. Therefore, the same type of decomposition applies independent of position in parameter space, in the region in question.
p-Ge electrically driven into the post-breakdown regime at liquid-He temperatures produces voltage oscillations which can be attributed to the formation of a chaotic attractor. Under variation of an applied magnetic field, a change in this attractor takes place which apparently reflects an increase in attractor dimensionality. A sequence of phase plots is presented which is interpreted as a transition from ordinary chaos to hyperchaos.
The linear correlation factor of spatially coupled nonlinear self-generated oscillations in the post-breakdown regime of p-Gc at 4.2 K is investigated. The observed results can be consistently explained in terms of a two-cell model of energy relaxation oscillations, which yields resonance transitions between correlated and anticorrelated oscillations. These are due to node-focus transitions of the fixed point of the passive cell which is slaved by the active cell.