Lower bounds on the Hausdorff dimension of the Rauzy gasket

ABSTRACT:

The Rauzy gasket is an important fractal object arising in several dynamical constructions, such as Novikov’s problem and some renormalization schemes for certain families of interval exchange maps. It was conjectured by Novikov and Maltsev in 2003 that the Hausdorff dimension D of the Rauzy gasket is strictly comprised between 1 and 2. In 2016, Avila, Hubert and Skripchenko confirmed the upper bound D<2. In this talk, I will explain how to use the thermodynamical results of Cao, Pesin and Zhao to show that D > 1.19. This is joint work with Carlos Matheus.

Posted on Nov 11, 2019 in Dynamical Systems, Seminars