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Dimension product structure of hyperbolic sets
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## Dimension product structure of hyperbolic sets

### Boris Hasselblatt and Jörg Schmeling

**Abstract.**
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
*

The copyright for this article reverts to public domain after 28 years from publication.

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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`

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