Self-affine sets with fibered tangents

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 $\mathcal{O}$ 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

References in corpus (3)

• Packing dimension and Ahlfors regularity of porous sets in metric spaces
• Separation conditions on controlled Moran constructions
• Micromeasure distributions and applications for conformally generated fractals

Cited by in corpus (3)

• Dimension of self-affine sets for fixed translation vectors
• Slices of the Takagi function
• Resonance between planar self-affine measures