Dimension and measures on sub-self-affine sets

Abstract

We show that in a typical sub-self-affine set, the Hausdorff and the Minkowski dimensions coincide and equal the zero of an appropriate topological pressure. This gives a partial positive answer to the question of Falconer. We also study the properties of the topological pressure and the existence and the uniqueness of natural measures supported on a sub-self-affine set.

References in corpus (3)

• Equilibrium states of the pressure function for products of matrices
• Overlapping self-affine sets of Kakeya type
• Separation conditions on controlled Moran constructions

Cited by in corpus (19)

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• On the coincidence of the Hausdorff and box dimensions for some affine-invariant sets