Genericity of dimension drop on self-affine sets

Abstract

We prove that generically, for a self-affine set in ${\mathbb{R}}^d$, removing one of the affine maps which defines the set results in a strict reduction of the Hausdorff dimension. This gives a partial positive answer to a folklore open question.

arXiv admin note: text overlap with arXiv:1609.07360

References in corpus (2)

• Dimension and measures on sub-self-affine sets
• Structure of equilibrium states on self-affine sets and strict monotonicity of affinity dimension

Cited by in corpus (2)

• Dimension of self-affine sets for fixed translation vectors
• Characterization for entropy of shifts of finite type on Cayley trees