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Tangents of invariant sets

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arxiv 2309.11971 v2 pith:5ZMBQWPZ submitted 2023-09-21 math.DS math.CAmath.MG

Antti Käenmäki , Alex Rutar This is my paper · ORCID
classification math.DSmath.CAmath.MG
keywords dimensionhausdorffsetsadditionalassouadassumptionattractorattractors
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We study the fine scaling properties of sets satisfying various weak forms of invariance. For general attractors of possibly overlapping bi-Lipschitz iterated function systems, we establish that the Assouad dimension is given by the Hausdorff dimension of a tangent at some point in the attractor. Under the additional assumption of self-conformality, we moreover prove that this property holds for a subset of full Hausdorff dimension.

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  1. Point-dimension theory (part II): The point-cross dimension

    math.MG 2026-07 conditional novelty 7.0 of 10

    A new pointwise invariant, the Point-Cross Dimension, quantifies the cumulative weighted complexity of independent directional channels through a single germ, separating directionality from isotropic dispersion.

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