On the structure of self-affine Jordan arcs in ℝ2

Abstract

We prove that if a self-affine arc γ∈R2\gamma \in {{\mathbb{R}}}^{2} does not satisfy weak separation condition, then it is a segment of a parabola or a straight line. If a self-affine arc γ\gamma is not a segment of a parabola or a line, then it is a component of the attractor of a Jordan multizipper with the same set of generators.

Keywords

• self-similar set
• self-affine jordan arc
• zipper
• weak separation property
• 28a80
• 26a27