Peter J. Olver School of Mathematics University of Minnesota
Fractalization and Quantization in Dispersive Systems and Lamb Oscillators
The evolution, through spatially periodic linear dispersion, of rough initial data leads to surprising quantized structures at rational times, and fractal, non-differentiable profiles at irrational times. Such phenomena, also known as the Talbot effect, have been encountered in a variety of dispersive wave models, in optics, and in quantum mechanics. I will present recent progress on the required analysis, on extensions to nonlinear wave models, and on the effect of coupling dispersive systems to Lamb oscillators.