TY - JOUR
T1 - Hausdorff dimension for horseshoes in ℝ3
AU - Simon, Károly
AU - Solomyak, Boris
PY - 1999/10
Y1 - 1999/10
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.
UR - http://www.scopus.com/inward/record.url?scp=0041154172&partnerID=8YFLogxK
U2 - 10.1017/s0143385799141671
DO - 10.1017/s0143385799141671
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SN - 0143-3857
VL - 19
SP - 1343
EP - 1363
JO - Ergodic Theory and Dynamical Systems
JF - Ergodic Theory and Dynamical Systems
IS - 5
ER -