When the Weak Separation Condition implies the Generalized Finite Type Condition

Abstract

We prove that an iterated function system of similarities on $\mathbb{R}$ that satisfies the weak separation condition and has an interval as its self-similar set satisfies the stronger generalized finite type condition. It is unknown if the assumption that the self-similar set is an interval is necessary.

14 pages, revised introduction

References in corpus (1)

• Box-counting fractal strings, zeta functions, and equivalent forms of Minkowski dimension

Cited by in corpus (2)

• Geometric and Combinatorial Properties of Self-similar Multifractal Measures
• Local Dimensions of Self-similar Measures Satisfying the Finite Neighbour Condition