Iterated function systems
Description
A common construction for fractal sets is to use an iterated function system, or IFS for short. One can associate with an IFS an invariant fractal set, as well as a family of invariant measures. This category includes my work on self-similar and self-affine sets, which includes dimension theory, multifractal analysis, and the study of separation conditions.
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Relevant Research Articles
- Assouad spectrum of Gatzouras–Lalley carpets
With: Amlan Banaji, Jonathan M. Fraser, István Kolossváry Journal: Preprint (submitted) Links: pdfarxiv - Tangents and pointwise Assouad dimension of invariant sets
With: Antti Käenmäki Journal: Preprint (submitted) Links: pdfarxiv - Interpolating with generalized Assouad dimensions
With: Amlan Banaji, Sascha Troscheit Journal: Preprint (submitted) Links: pdfarxiv - Assouad-type dimensions of overlapping self-affine sets
With: Jonathan M. Fraser Journal: Ann. Fenn. Math. 49 (2024), 3–21 Links: pdfdoizblarxiv - A multifractal decomposition for self-similar measures with exact overlaps
Journal: Preprint (submitted) Links: pdfarxiv - Local dimensions of self-similar measures satisfying the Finite Neighbour Condition
With: Kathryn E. Hare Journal: Nonlinearity 35 (2022), 4876–4904 Links: pdfdoizblarxiv - Geometric and combinatorial properties of self-similar multifractal measures
Journal: Ergodic Theory Dyn. Syst. 43 (2023), 2028–2072 Links: pdfdoizblarxiv - When the Weak Separation Condition implies the Generalized Finite Type Condition
With: Kathryn E. Hare, Kevin G. Hare Journal: Proc. Amer. Math. Soc. 149 (2021), 1555–1568 Links: pdfdoizblarxiv