A short existence proof for correlation dimension
type: Item
instance of: scholarly article
title: A short existence proof for correlation dimension
zbMATH Open document ID: 0959.37006
DOI: 10.1023/A:1023253709865
author: Anthony Manning
author: Károly Simon
published in: Journal of Statistical Physics
publication date: 2001-04-24T00:00:00Z
review text: The subject of investigation is the correlation dimension introduced in the work of \textit{I.~Procaccia, P.~Grassberger}, and \textit{V.~G.~E.~Hentschel} [Lect. Notes Phys. 179, 212-221 (1983)] and put on a rigorous basis by \textit{Ya.~Pesin} and \textit{A.~Tempelman} [Random Comput. Dyn. 3, 137-156 (1995; Zbl 0833.60008)]. The theorem by Pesin and Tempelman that is fundamental for precise definition of the correlation dimension asserts that this dimension is given in terms of the measure of neighborhoods of the diagonal. The paper presents a short and more simple proof of this existence theorem.
reviewed by: Eugene Ershov
Mathematics Subject Classification ID: 37A25
Mathematics Subject Classification ID: 37D45
zbMATH DE Number: 1279388
zbMATH Keywords: correlation dimension
zbMATH Keywords: ergodic measure
zbMATH Keywords: neighborhood of diagonal
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1279388