Nontrivial fractals in the plane and linear operators with joint spectral radius equal to 1
type: Item
instance of: scholarly article
title: Nontrivial fractals in the plane and linear operators with joint spectral radius equal to 1
zbMATH Open document ID: 0938.37028
DOI: 10.1007/BF02312855
published in: Mathematical Notes
publication date: 2000-06-27T00:00:00Z
review text: Properties of invariant bodies of a family of linear operators \(A_1,\dots,A_k:\mathbb{R}^n\to\mathbb{R}^n\) have been studied in the paper [\textit{V. Yu. Protasov}, Fundam. Prikl. Mat. 2, No. 1, 205-231 (1996; Zbl 0899.47002)], which also contains an algorithm that calculates the joint spectral radius of these operators. In the examples considered in the paper of Protasov (loc. cit), the dimensions (both topological and Hausdorff) of the invariant sets on the plane are equal to either 0 or 1. The main goal of this paper is to construct a class of operators with invariant sets having fractional Hausdorff dimension.
Mathematics Subject Classification ID: 37F35
Mathematics Subject Classification ID: 47A10
zbMATH DE Number: 1262513
zbMATH Keywords: fractal sets
zbMATH Keywords: linear operators
zbMATH Keywords: Hausdorff dimension
zbMATH Keywords: spectral radius
zbMATH Keywords: topological dimension
zbMATH Keywords: invariant sets
author: I. A. Sheipak
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
cites work: Q3731958
cites work: Iterated function systems and the global construction of fractals
description: scientific article; zbMATH DE number 1262513