Packing dimension estimation for exceptional parameters
type: Item
instance of: scholarly article
title: Packing dimension estimation for exceptional parameters
zbMATH Open document ID: 1005.37008
DOI: 10.1007/BF02764074
author: M. Rams
published in: Israel Journal of Mathematics
publication date: 2002-11-03T00:00:00Z
review text: Let \(V\) be an open and bounded subset of \(\mathbb{R}^d\). For each parameter \(t\in \overline{V}\) we consider a conformal iterated function system (IFS) \((f_i(\cdot, t))_{i=1}^k\) in \(\mathbb{R}^d\) depending on the parameter \(t\). By assuming this dependence to be smooth, the author proves: For each \(p\), let \(G_p= \{t\in \overline{V}: \dim_H \Lambda_t\leq p\}\), here \(\Lambda_t\) denotes the limit set of the IFS. If the IFS satisfies the transversality condition and \(p< \min(d,s(u))\), then \[ \limsup_{r\to 0} \dim_p (G_p\cap B_r(u))\leq p, \] where \(s(u)\) denotes the solution of Bowen's equation.
reviewed by: Jianyong Qiao
Mathematics Subject Classification ID: 37C45
Mathematics Subject Classification ID: 28A80
Mathematics Subject Classification ID: 37F99
zbMATH DE Number: 1799790
zbMATH Keywords: packing dimension
zbMATH Keywords: conformal iterated function system
zbMATH Keywords: Bowen's equation
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02764074
OpenAlex ID: W2019123118
description: scientific article; zbMATH DE number 1799790