Self-affine sets with fibred 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.