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.