Local estimates for the Hausdorff dimension of an attractor
type: Item
instance of: scholarly article
title: Local estimates for the Hausdorff dimension of an attractor
zbMATH Open document ID: 0714.58035
DOI: 10.1016/0022-247X(90)90198-O
author: D. Kharzeev
published in: Journal of Mathematical Analysis and Applications
publication date: 1990-01-01T00:00:00Z
review text: In the paper a continuous nonlinear semigroup acting on a separable Hilbert space is considered. It is assumed that the semigroup admits a compact global attractor on which it is bijective. In this context local and global Lyapunov exponents are defined and used to introduce the Douady-Oesterlé dimension. It is shown the existence of a critical path in the attractor for which the local Douady-Oesterlé dimension dominates the Hausdorff dimension of the attractor. An example for a Lorenz type equation is given.
Mathematics Subject Classification ID: 37C70
Mathematics Subject Classification ID: 35-XX
zbMATH DE Number: 4176065
zbMATH Keywords: dissipative nonlinear PDE's
zbMATH Keywords: attractor
zbMATH Keywords: Hausdorff dimension
reviewed by: Marian Mrozek
MaRDI profile type: Publication
cites work: Solution d'un problème sur les itérés d'un opérateur positif sur \(\mathcal C(K)\), et propriétés de moyennes associées
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cites work: Attractors representing turbulent flows
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cites work: Infinite-dimensional dynamical systems in mechanics and physics
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description: scientific article; zbMATH DE number 4176065