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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.05078 |
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| _version_ | 1866917464836669440 |
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| author | Zhang, Junda |
| author_facet | Zhang, Junda |
| contents | We concern the structrue of generating weighted IFSs of a self-similar measure on the real line. We provide various sufficient conditions for the existence of a minimal generating weighted IFS of a self-similar measure on the real line. Under the homogeneity, we show that `most' self-similar measures on the real line have a minimal generating weighted IFS, without separation conditions. The ingredients of our proofs are based on the zero distribution and factorization theory of exponential polynomials, logarithmic commensurability (with a dynamical system argument), and results on the structure of generating IFSs of a self-similar sets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_05078 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the minimal generating weighted IFS of self-similar measure Zhang, Junda Dynamical Systems 28A80 We concern the structrue of generating weighted IFSs of a self-similar measure on the real line. We provide various sufficient conditions for the existence of a minimal generating weighted IFS of a self-similar measure on the real line. Under the homogeneity, we show that `most' self-similar measures on the real line have a minimal generating weighted IFS, without separation conditions. The ingredients of our proofs are based on the zero distribution and factorization theory of exponential polynomials, logarithmic commensurability (with a dynamical system argument), and results on the structure of generating IFSs of a self-similar sets. |
| title | On the minimal generating weighted IFS of self-similar measure |
| topic | Dynamical Systems 28A80 |
| url | https://arxiv.org/abs/2605.05078 |