On the dimension of deterministic and random Cantor-like sets
type: Item
instance of: scholarly article
title: On the dimension of deterministic and random Cantor-like sets
zbMATH Open document ID: 0834.28004
author: Howard Weiss
author: Yakov Pesin
published in: Mathematical Research Letters
publication date: 1996-03-31T00:00:00Z
review text: The authors extend Moran's construction of fractals to an asymptotic, respectively random type construction. In the first case the contraction ratios converge in a certain Cesàro-like mean to zero. The random construction is determined by an ergodic stationary process. They unify results concerning box and Hausdorff dimension known for deterministic and random Cantor-like sets. The constructions involve only weak restrictions on the geometry.
Mathematics Subject Classification ID: 28A80
Mathematics Subject Classification ID: 60D05
Mathematics Subject Classification ID: 28A78
zbMATH DE Number: 817716
zbMATH Keywords: box dimension
zbMATH Keywords: fractals
zbMATH Keywords: Moran's construction
zbMATH Keywords: ergodic stationary process
zbMATH Keywords: Hausdorff dimension
zbMATH Keywords: random Cantor-like sets
reviewed by: Hermann Haase
MaRDI profile type: Publication
full work available at URL: mrl.1994.v1.n4.a12
OpenAlex ID: W1982311379
DOI: 10.4310/MRL.1994.V1.N4.A12
description: scientific article; zbMATH DE number 817716