Self-affine sets with fibered tangents
| Autor: | Eino Rossi, Henna Koivusalo, Antti Käenmäki |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2015 |
| Předmět: |
Pure mathematics
Class (set theory) General Mathematics Dynamical Systems (math.DS) Interval (mathematics) iterated function system 01 natural sciences self-affine set Generic point Line segment strictly self-affine sets 0103 physical sciences Classical Analysis and ODEs (math.CA) FOS: Mathematics Point (geometry) Porous set 0101 mathematics Mathematics - Dynamical Systems Mathematics Applied Mathematics 010102 general mathematics ta111 Tangent tangent sets Tangent set Mathematics - Classical Analysis and ODEs 010307 mathematical physics Affine transformation |
| Zdroj: | Kaenmaki, A, Koivusalo, H L L & Rossi, E 2017, ' Self-affine sets with fibred tangents ', Ergodic Theory Dynamical Systems, vol. 37, no. 6, pp. 1915–1934 . https://doi.org/10.1017/etds.2015.130 |
| Popis: | We study tangent sets of strictly self-affine sets in the plane. If a set in this class satisfies the strong separation condition and projects to a line segment for sufficiently many directions, then for each generic point there exists a rotation $\mathcal O$ such that all tangent sets at that point are either of the form $\mathcal O((\mathbb R \times C) \cap B(0,1))$, where $C$ is a closed porous set, or of the form $\mathcal O((\ell \times \{ 0 \}) \cap B(0,1))$, where $\ell$ is an interval. 17 pages, 5 figures |
| Databáze: | OpenAIRE |
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