Mercredi 1 Décembre
Heure: 
13:30  15:00 
Lieu: 
Salle B405, bâtiment B, LAGA, Institut Galilée, Université Paris 13 
Résumé: 
Théorie Ergodique et Systèmes Dynamiques  Dimensions of 'selfaffine sponges' invariant under the action of multiplicative integers  
Description: 
Guilhem Brunet Let $m_1 geq m_2 geq 2$ be integers. We consider particular subsets of the product symbolic sequence space $({0,cdots,m_11} imes {0,cdots,m_21})^{mathbb{N}^*}$ that are invariant under the action of the semigroup of multiplicative integers. These sets are defined following Kenyon, Peres and Solomyak. We compute the Hausdorff and Minkowski dimensions of the projection of these sets onto an affine grid of the unit square. The proof of our Hausdorff dimension formula proceeds via a variational principle over some class of Borel probability measures on the studied sets. This extends wellknown results on selfaffine Sierpi'nski carpets, as well as the onedimensional study of the three mentioned authors. We then generalize our results to the same subsets defined in dimension $d geq 2$. 

