Self-affine sets with fibred tangents

Antti Kaenmaki; Henna L L Koivusalo; Eino Rossi

doi:10.1017/etds.2015.130

Self-affine sets with fibred tangents

Antti Kaenmaki, Henna L L Koivusalo, Eino Rossi

School of Mathematics

Research output: Contribution to journal › Article (Academic Journal) › peer-review

9 Citations (Scopus)

53 Downloads (Pure)

Abstract

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 O such that all tangent sets at that point are either of the form O((R × C) ∩ B(0, 1)), where C is a closed porous
set, or of the form O((` × {0}) ∩ B(0, 1)), where ` is an interval.

Original language	English
Pages (from-to)	1915–1934
Number of pages	20
Journal	Ergodic Theory Dynamical Systems
Volume	37
Issue number	6
Early online date	28 Jan 2016
DOIs	https://doi.org/10.1017/etds.2015.130
Publication status	Published - 1 Sept 2017

Keywords

Tangent set
self-affine set
iterated function system

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10.1017/etds.2015.130

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This is the author accepted manuscript (AAM). The final published version (version of record) is available online via Cambridge University Press at https://doi.org/10.1017/etds.2015.130 . Please refer to any applicable terms of use of the publisher.
Accepted author manuscript, 491 KBLicence: CC BY-NC-ND

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Dr Henna L L Koivusalo
- henna.koivusalobristol.acuk
- School of Mathematics - Senior Lecturer
Person: Academic

Cite this

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abstract = "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 O such that all tangent sets at that point are either of the form O((R × C) ∩ B(0, 1)), where C is a closed porousset, or of the form O((` × {0}) ∩ B(0, 1)), where ` is an interval.",

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AU - Rossi, Eino

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N2 - 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 O such that all tangent sets at that point are either of the form O((R × C) ∩ B(0, 1)), where C is a closed porousset, or of the form O((` × {0}) ∩ B(0, 1)), where ` is an interval.

AB - 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 O such that all tangent sets at that point are either of the form O((R × C) ∩ B(0, 1)), where C is a closed porousset, or of the form O((` × {0}) ∩ B(0, 1)), where ` is an interval.

KW - Tangent set

KW - self-affine set

KW - iterated function system

U2 - 10.1017/etds.2015.130

DO - 10.1017/etds.2015.130

M3 - Article (Academic Journal)

SN - 0143-3857

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SP - 1915

EP - 1934

JO - Ergodic Theory Dynamical Systems

JF - Ergodic Theory Dynamical Systems

IS - 6

ER -

Self-affine sets with fibred tangents

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Dr Henna L L Koivusalo

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