6533b821fe1ef96bd127b83c

RESEARCH PRODUCT

Self-affine sets with fibered tangents

Eino RossiHenna KoivusaloAntti Käenmäki

subject

Pure mathematicsClass (set theory)General MathematicsDynamical Systems (math.DS)Interval (mathematics)iterated function system01 natural sciencesself-affine setGeneric pointLine segmentstrictly self-affine sets0103 physical sciencesClassical Analysis and ODEs (math.CA)FOS: MathematicsPoint (geometry)Porous set0101 mathematicsMathematics - Dynamical SystemsMathematicsApplied Mathematics010102 general mathematicsta111Tangenttangent setsTangent setMathematics - Classical Analysis and ODEs010307 mathematical physicsAffine transformation

description

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.

yearjournalcountryeditionlanguage
2016-01-28
10.1017/etds.2015.130http://arxiv.org/abs/1505.00958