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Self-affine sets with fibred tangents

Published online by Cambridge University Press:  28 January 2016

ANTTI KÄENMÄKI ,
HENNA KOIVUSALO  and
EINO ROSSI
ANTTI KÄENMÄKI
Affiliation:
University of Jyväskylä, Department of Mathematics and Statistics, P.O. Box 35 (MaD), FI-40014 University of Jyväskylä, Finland email [email protected], [email protected]
HENNA KOIVUSALO
Affiliation:
Department of Mathematics, University of York, Heslington, York YO10 5DD, UK email [email protected]
EINO ROSSI
Affiliation:
University of Jyväskylä, Department of Mathematics and Statistics, P.O. Box 35 (MaD), FI-40014 University of Jyväskylä, Finland email [email protected], [email protected]
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Abstract

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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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 37 , Issue 6 , September 2017 , pp. 1915 - 1934
Copyright
© Cambridge University Press, 2016 

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