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We conjecture that the fractal dimension of hyperbolic sets can be computed by adding those of their stable and unstable slices. This would facilitate substantial progress in the calculation or estimation of these dimensions, which are related in deep ways to dynamical properties. We prove the conjecture in a model case of Smale solenoids.

Copyright 2004 American Mathematical Society
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Article Info

• ERA Amer. Math. Soc. 10 (2004), pp. 88-96
• Publisher Identifier: S 1079-6762(04)00133-7
• 2000 Mathematics Subject Classification. Primary 37D10; Secondary 37C35
• Key words and phrases. Hyperbolic set, fractal dimension, Hausdorff dimension, Eckmann-Ruelle conjecture, holonomies, Lipschitz continuity, product structure
• Received by editors June 8, 2004
• Posted on August 26, 2004
• Communicated by Svetlana Katok
• Comments (When Available)

Boris Hasselblatt

Department of Mathematics, Tufts University, Medford, MA 02155

E-mail address: bhasselb@tufts.edu

Jörg Schmeling

Lund Institute of Technology, Lunds Universitet, Box 118, SE-22100 Lund, Sweden

E-mail address: Jorg.Schmeling@math.lth.se