Hausdorff dimension of the Rauzy gasket

Natalia Jurga (University of St Andrews)

Thursday 11th January 16:00-17:00 Maths 311B

Abstract

The Rauzy gasket, which is the attractor of an iterated function system on the projective plane, is an important subset of parameter space in numerous dynamical and topological problems. Arnoux conjectured that the Hausdorff dimension of the Rauzy gasket is strictly less than 2, and since then there has been considerable interest in computing its Hausdorff dimension. After introducing the set and discussing its history, we will show how recent developments in the theory of self-affine sets and measures can be adapted to compute the Hausdorff dimension of the Rauzy gasket.

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