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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 'self-affine 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 $({0,cdots,m_1-1} imes
{0,cdots,m_2-1})^{mathbb{N}^*}$ 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 well-known
results on self-affine Sierpi'nski carpets, as well as the
one-dimensional study of the three mentioned authors. We then generalize
our results to the same subsets defined in dimension $d geq 2$. |
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