Hausdorff dimension for horseshoes in ℝ3

Károly Simon; Boris Solomyak

doi:10.1017/s0143385799141671

Hausdorff dimension for horseshoes in ℝ³

Károly Simon
, Boris Solomyak

Research output: Contribution to journal › Article › peer-review

26 Scopus citations

Abstract

Using pressure formulas we compute the Hausdorff dimension of the basic set of 'almost every' C^1+α horseshoe map in ℝ³ of the form F(x, y, z) = (γ(x, z), τ(y, z), ψ(z)), where |ψ′| > 1 and 0 < |γ′_x|, |τ′_y| < 1/2 on the basic set. Similar results are obtained for attractors of nonlinear 'baker's maps' in ℝ³.

Original language	English
Pages (from-to)	1343-1363
Number of pages	21
Journal	Ergodic Theory and Dynamical Systems
Volume	19
Issue number	5
DOIs	https://doi.org/10.1017/s0143385799141671
State	Published - Oct 1999
Externally published	Yes

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title = "Hausdorff dimension for horseshoes in ℝ3",

abstract = "Using pressure formulas we compute the Hausdorff dimension of the basic set of 'almost every' C1+α horseshoe map in ℝ3 of the form F(x, y, z) = (γ(x, z), τ(y, z), ψ(z)), where |ψ′| > 1 and 0 < |γ′x|, |τ′y| < 1/2 on the basic set. Similar results are obtained for attractors of nonlinear 'baker's maps' in ℝ3.",

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N2 - Using pressure formulas we compute the Hausdorff dimension of the basic set of 'almost every' C1+α horseshoe map in ℝ3 of the form F(x, y, z) = (γ(x, z), τ(y, z), ψ(z)), where |ψ′| > 1 and 0 < |γ′x|, |τ′y| < 1/2 on the basic set. Similar results are obtained for attractors of nonlinear 'baker's maps' in ℝ3.

AB - Using pressure formulas we compute the Hausdorff dimension of the basic set of 'almost every' C1+α horseshoe map in ℝ3 of the form F(x, y, z) = (γ(x, z), τ(y, z), ψ(z)), where |ψ′| > 1 and 0 < |γ′x|, |τ′y| < 1/2 on the basic set. Similar results are obtained for attractors of nonlinear 'baker's maps' in ℝ3.

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JO - Ergodic Theory and Dynamical Systems

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Hausdorff dimension for horseshoes in ℝ³

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