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ISSN 1079-6762

 

Dimension product structure of hyperbolic sets


Authors: Boris Hasselblatt and Jörg Schmeling
Journal: Electron. Res. Announc. Amer. Math. Soc. 10 (2004), 88-96
MSC (2000): Primary 37D10; Secondary 37C35
Published electronically: August 26, 2004
MathSciNet review: 2084468
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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.


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Additional Information

Boris Hasselblatt
Affiliation: Department of Mathematics, Tufts University, Medford, MA 02155
Email: bhasselb@tufts.edu

Jörg Schmeling
Affiliation: Lund Institute of Technology, Lunds Universitet, Box 118, SE-22100 Lund, Sweden
Email: Jorg.Schmeling@math.lth.se

DOI: http://dx.doi.org/10.1090/S1079-6762-04-00133-7
PII: S 1079-6762(04)00133-7
Keywords: Hyperbolic set, fractal dimension, Hausdorff dimension, Eckmann-Ruelle conjecture, holonomies, Lipschitz continuity, product structure
Received by editor(s): June 8, 2004
Published electronically: August 26, 2004
Communicated by: Svetlana Katok
Article copyright: © Copyright 2004 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.