Separation conditions on controlled Moran constructions

Abstract

It is well known that the open set condition and the positivity of the $t$-dimensional Hausdorff measure are equivalent on self-similar sets, where $t$ is the zero of the topological pressure. We prove an analogous result for a class of Moran constructions and we study different kinds of Moran constructions with this respect.

Cited by in corpus (15)

• Packing dimension and Ahlfors regularity of porous sets in metric spaces
• Dimension and measures on sub-self-affine sets
• Weak separation condition, Assouad dimension, and Furstenberg homogeneity
• Overlapping self-affine sets of Kakeya type
• Measures with predetermined regularity and inhomogeneous self-similar sets
• Self-conformal sets with positive Hausdorff measure
• Local dimensions in Moran constructions
• Local Dimensions of Measures on Infinitely Generated Self-Affine Sets
• Directed porosity on conformal iterated function systems and weak convergence of singular integrals
• Self-affine sets with fibered tangents
• Ahlfors regularity and fractal dimension of Smale spaces
• Conformal graph directed Markov systems on Carnot groups
• A note on correlation and local dimensions
• Local conical dimensions for measures
• Regularity of non-autonomous self-similar sets