Lower bounds on the Hausdorff dimension of the Rauzy gasket
Carlos Matheus Silva Santos (Ecole Polytechnic/CNRS)
Thursday 28th November, 2019 16:00-17:00 Maths 311B
Abstract
The classical thermodynamical formalism of Ruelle, Bowen, ... is a beautiful theory allowing to treat several natural questions including the computation of the Hausdorff dimension of conformal repellers in terms of the spectral features of certain transfer operators.
Nevertheless, the problem of giving bounds for the Hausdorff dimension of non-conformal repellers arises naturally in many contexts. In this talk, we describe a joint work with Rodolfo Gutierrez-Romo where a lower bound on the Hausdorff dimension of the Rauzy gasket (a fractal set related to Novikov's problem on the trajectories of electrons in metals) is obtained via some recent results from subadditive thermodynamical formalism.
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