Assouad dimension of planar self-affine sets
| Autor: | Balázs Bárány, Antti Käenmäki, Eino Rossi |
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| Přispěvatelé: | Department of Mathematics and Statistics |
| Rok vydání: | 2020 |
| Předmět: |
Pure mathematics
Assouad dimension General Mathematics Dynamical Systems (math.DS) 01 natural sciences Measure (mathematics) Conformal dimension Self-affine set Mathematics - Metric Geometry conformal dimension Dimension (vector space) Projection (mathematics) Simple (abstract algebra) Classical Analysis and ODEs (math.CA) FOS: Mathematics 111 Mathematics CARPETS Mathematics - Dynamical Systems 0101 mathematics Mathematics Applied Mathematics 010102 general mathematics Tangent Metric Geometry (math.MG) LIMIT-SETS Primary 28A80 Secondary 37C45 37L30 Mathematics - Classical Analysis and ODEs Hausdorff dimension tangent set Affine transformation HAUSDORFF DIMENSION LEDRAPPIER-YOUNG FORMULA |
| Zdroj: | Transactions of the American Mathematical Society. 374:1297-1326 |
| ISSN: | 1088-6850 0002-9947 |
| Popis: | We calculate the Assouad dimension of a planar self-affine set $X$ satisfying the strong separation condition and the projection condition and show that $X$ is minimal for the conformal Assouad dimension. Furthermore, we see that such a self-affine set $X$ adheres to very strong tangential regularity by showing that any two points of $X$, which are generic with respect to a self-affine measure having simple Lyapunov spectrum, share the same collection of tangent sets. 25 pages, 2 figures; added Example 3.3, improved presentation |
| Databáze: | OpenAIRE |
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