Self-affine sets with fibred tangents

Antti Kaenmaki, Henna L L Koivusalo, Eino Rossi

Research output: Contribution to journalArticle (Academic Journal)peer-review

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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 porous
set, or of the form O((` × {0}) ∩ B(0, 1)), where ` is an interval.
Original languageEnglish
Pages (from-to)1915–1934
Number of pages20
JournalErgodic Theory Dynamical Systems
Volume37
Issue number6
Early online date28 Jan 2016
DOIs
Publication statusPublished - 1 Sep 2017

Keywords

  • Tangent set
  • self-affine set
  • iterated function system

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