# Dimensions of ‘self-affine sponges’ invariant under the action of multiplicative integers

@article{Brunet2021DimensionsO, title={Dimensions of ‘self-affine sponges’ invariant under the action of multiplicative integers}, author={Guilhem Brunet}, journal={Ergodic Theory and Dynamical Systems}, year={2021} }

Let
$m_1 \geq m_2 \geq 2$
be integers. We consider subsets of the product symbolic sequence space
$(\{0,\ldots ,m_1-1\} \times \{0,\ldots ,m_2-1\})^{\mathbb {N}^*}$
that are invariant under the action of the semigroup of multiplicative integers. These sets are defined following Kenyon, Peres, and Solomyak and using a fixed integer
$q \geq 2$
. We compute the Hausdorff and Minkowski dimensions of the projection of these sets onto an affine grid of the unit…

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