Search results for "products of matrices"

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Genericity of dimension drop on self-affine sets

2017

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.

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 UncertaintyStatistics & Probability Letters
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