Hausdorff dimension of attractors for two dimensional Lorenz transformations
type: Item
instance of: scholarly article
title: Hausdorff dimension of attractors for two dimensional Lorenz transformations
zbMATH Open document ID: 0952.37004
DOI: 10.1007/BF02773221
author: Thomas Steinberger
published in: Israel Journal of Mathematics
publication date: 2000-09-19T00:00:00Z
review text: The author considers the two-dimensional Lorenz transformation \[ F(x, y) = (T(x), g(x,y)), \] where \(T\) is a piecewise monotonic topologically transitive and expanding transformation on \([0, 1],\) \(g(x, y): [0, 1]^2 \to [0, 1]\) is piecewise differentiable. It is proved that the Hausdorff dimension of the attractor of \(F\) equals \(z+1\) where \(z\) is the unique zero of the pressure function \(t \to p(F, t\varphi)\), \(\varphi = \log |\partial g / \partial y|\).
Mathematics Subject Classification ID: 37C70
Mathematics Subject Classification ID: 37B25
zbMATH DE Number: 1445783
zbMATH Keywords: Lorenz transformation
zbMATH Keywords: attractor
zbMATH Keywords: Hausdorff dimension
reviewed by: Victor I. Tkachenko
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1445783