Quantitative recurrence properties and homogeneous self-similar sets
| Autor: | Min Wu, Yuanyang Chang, Wen Wu |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Mathematics - Number Theory
Series (mathematics) Applied Mathematics General Mathematics Null (mathematics) Dynamical Systems (math.DS) Positive function Measure (mathematics) Combinatorics 28A80 28D05 11K55 Homogeneous Metric (mathematics) FOS: Mathematics Hausdorff measure Number Theory (math.NT) Mathematics - Dynamical Systems Divergence (statistics) Mathematics |
| Zdroj: | Proceedings of the American Mathematical Society. 147:1453-1465 |
| ISSN: | 1088-6826 0002-9939 |
| Popis: | Let $K$ be a homogeneous self-similar set satisfying the strong separation condition. This paper is concerned with the quantitative recurrence properties of the natural map $T: K\rightarrow K$ induced by the shift. Let $\mu$ be the natural self-similar measure supported on $K$. For a positive function $\varphi$ defined on $\mathbb{N}$, we show that the $\mu$-measure of the following set \begin{equation*} R(\varphi):=\{x\in K: |T^n x-x Comment: 12 pages |
| Databáze: | OpenAIRE |
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