Hölder spiral arcs
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
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| _version_ | 1866913966749384704 |
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| author | Garitsis, Efstathios Konstantinos Chrontsios Vellis, Vyron |
| author_facet | Garitsis, Efstathios Konstantinos Chrontsios Vellis, Vyron |
| contents | We establish a quantitative necessary and sufficient condition for a spiral arc to be a Hölder arc. The class of spiral arcs contains the polynomial spirals studied by Fraser, and the elliptical spirals studied by Burrell-Falconer-Fraser. As an application, we recover the sharp result on the Hölder winding problem for polynomial spirals. Moreover, we provide a sharp exponent estimate for the Hölder classification of polynomial spirals, which coincides with the corresponding quasiconformal classification estimate, and improve certain exponent bounds of Burrell-Falconer-Fraser on the Hölder classification of elliptical spirals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_18788 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hölder spiral arcs Garitsis, Efstathios Konstantinos Chrontsios Vellis, Vyron Classical Analysis and ODEs Dynamical Systems We establish a quantitative necessary and sufficient condition for a spiral arc to be a Hölder arc. The class of spiral arcs contains the polynomial spirals studied by Fraser, and the elliptical spirals studied by Burrell-Falconer-Fraser. As an application, we recover the sharp result on the Hölder winding problem for polynomial spirals. Moreover, we provide a sharp exponent estimate for the Hölder classification of polynomial spirals, which coincides with the corresponding quasiconformal classification estimate, and improve certain exponent bounds of Burrell-Falconer-Fraser on the Hölder classification of elliptical spirals. |
| title | Hölder spiral arcs |
| topic | Classical Analysis and ODEs Dynamical Systems |
| url | https://arxiv.org/abs/2502.18788 |