Institut für Mathematik


Modul:   MAT760  Ergodic theory and dynamical systems seminar

Hausdorff dimension of the Rauzy gasket

Vortrag von Dr. Natalia Jurga

Sprecher eingeladen von: Prof. Dr. Corinna Ulcigrai

Datum: 22.05.23  Zeit: 13.30 - 14.30  Raum: ETH HG G 43

The Rauzy gasket is a fractal subset of the two dimensional simplex which 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. In this talk we will also discuss a natural class of measures supported on the Rauzy gasket (the stationary measures for the projective action of the generators of the Rauzy gasket). We will show how recent developments from the theory of self-affine sets can be adapted to compute the dimension of these measures, which will allow us to establish an exact value for the Hausdorff dimension of the Rauzy gasket.