%0 Journal Article
%T On a class of sofic affine invariant subsets of the 2-torus related to an Erdős problem
%+ Institut de Mathématiques de Marseille (I2M)
%A Olivier, Eric
%< avec comité de lecture
%@ 0026-9255
%J Monatshefte für Mathematik
%I Springer Verlag
%V 165
%N 3-4
%P 447--497
%8 2012-03
%D 2012
%R 10.1007/s00605-011-0296-2
%Z Mathematics [math]/Number Theory [math.NT]Journal articles
%X Let 1 β G be the closed projection on the 2-torus of the (modified) Rademacher graph in base β. The smallest compact containing G and left invariant by the diagonal endomorphism $${(x,y)\mapsto(2x,\beta y)}$$ (mod 1) is denoted by K. For β a simple Parry number of PV-type, K is proved to be a sofic affine invariant set with a fractal geometry closed to the one of G. When β is the golden number, we prove the uniqueness of the measure with full Hausdorff dimension on K.
%G English
%L hal-01387010
%U https://hal.science/hal-01387010
%~ CNRS
%~ UNIV-AMU
%~ EC-MARSEILLE
%~ INSMI
%~ I2M
%~ I2M-2014-