Maximum local Lyapunov dimension bounds the box dimension. Direct proof for invariant sets on Riemannian manifolds
type: Item
instance of: scholarly article
title: Maximum local Lyapunov dimension bounds the box dimension. Direct proof for invariant sets on Riemannian manifolds
zbMATH Open document ID: 1137.37308
DOI: 10.4171/ZAA/1162
author: Katrin Gelfert
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 2004-05-27T00:00:00Z
review text: Summary: For a \(C^1\) map \(\phi\) on a Riemannian manifold and for a compact invariant set \(K\) it is proved that the maximal local Lyapunov dimension of \(\phi\) on \(K\) bounds the box dimension of \(K\) from above. A version for Hilbert spaces is also presented. The introduction of an adapted Riemannian metric provides in a certain sense an optimal upper bound for the box dimension of the Lorenz attractor.
Mathematics Subject Classification ID: 37C45
Mathematics Subject Classification ID: 37C70
Mathematics Subject Classification ID: 37L30
zbMATH DE Number: 2068756
Wikidata QID: Q115211784
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.4171/zaa/1162
OpenAlex ID: W2090702751
description: scientific article; zbMATH DE number 2068756