6533b824fe1ef96bd128003d

RESEARCH PRODUCT

Genericity of dimension drop on self-affine sets

Bing LiAntti Käenmäki

subject

Statistics and ProbabilityPure mathematicsthermodynamic formalismDynamical Systems (math.DS)01 natural sciencesself-affine setsingular value functionAffine combinationAffine hullClassical Analysis and ODEs (math.CA)FOS: MathematicsMathematics - Dynamical Systems0101 mathematicsMathematicsDiscrete mathematicsta111010102 general mathematicsMinkowski–Bouligand dimensionproducts of matricesEffective dimension010101 applied mathematicsAffine coordinate systemMathematics - Classical Analysis and ODEsHausdorff dimensionAffine transformationStatistics Probability and Uncertainty

description

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.

yearjournalcountryeditionlanguage
2017-01-01Statistics & Probability Letters
https://doi.org/10.1016/j.spl.2017.02.028