Philipp Gohlke (Jena)
Abstract: The Pisot substitution conjecture states that for an appropriate class of substitutions the corresponding dynamical systems have pure point spectrum, and can therefore be represented by group rotations. A natural geometric representation of such a group rotation is given by the Rauzy fractal associated to a Pisot substitution. In the setting of random substitutions the spectrum is generally richer, but the idea of Rauzy fractals can still be used to find a generic equicontinuous factor. We will also discuss how the concept of a Rauzy measure can help us to interpolate between the Rauzy fractals of (deterministic) substitutions.
