A sequential view of self--similar measures, or, What the ghosts of Mahler and Cantor can teach us about dimension

zbMath1460.28007arXiv2011.10722MaRDI QIDQ5856387

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Publication date: 26 March 2021

Full work available at URL: https://arxiv.org/abs/2011.10722

zbMATH Keywords

Hausdorff dimensioniterated function systemautomatic sequenceMahler functionself-affine set

Mathematics Subject Classification ID

Metric theory of other algorithms and expansions; measure and Hausdorff dimension (11K55) Fractals (28A80) Automata sequences (11B85) Quasicrystals and aperiodic tilings in discrete geometry (52C23)

Related Items (2)

Spectral theory of regular sequences ⋮ The Ghost Measures of Affine Regular Sequences

Cites Work

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• The ring of \(k\)-regular sequences
• Asymptotic expansions for Fourier transform of singular self-affine measures
• Limit sets of automatic sequences.
• Algebraic Independence of Mahler Functions via Radial Asymptotics
• An analogue of Cobham’s theorem for fractals
• Transcendence tests for Mahler functions
• Projections on Invariant Subspaces
• VON KOCH AND THUE-MORSE REVISITED
• Self-Similar Measures and Their Fourier Transforms. II
• Automatic Sequences
• A natural probability measure derived from Stern’s diatomic sequence
• The Ghost Measures of Affine Regular Sequences
• An asymptotic approach in Mahler's method

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