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Dimension product structure of hyperbolic sets

Hasselblatt, B and Schmeling, Jörg LU (2004) In Electronic Research Announcements of the American Mathematical Society 10. p.88-96
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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author
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organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Lipschitz continuity, holonomies, conjecture, Eckmann-Ruelle, Hausdorff dimension, hyperbolic set, fractal dimension, product structure
in
Electronic Research Announcements of the American Mathematical Society
volume
10
pages
88 - 96
publisher
American Mathematical Society (AMS)
external identifiers
  • wos:000223768700010
  • scopus:15944367479
ISSN
1079-6762
DOI
10.1090/S1079-6762-04-00133-7
language
English
LU publication?
yes
id
c5f7b9e5-094f-468f-b0f4-dbe5442e16c5 (old id 268192)
date added to LUP
2016-04-01 15:59:47
date last changed
2022-03-14 21:25:55
@article{c5f7b9e5-094f-468f-b0f4-dbe5442e16c5,
  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.}},
  author       = {{Hasselblatt, B and Schmeling, Jörg}},
  issn         = {{1079-6762}},
  keywords     = {{Lipschitz continuity; holonomies; conjecture; Eckmann-Ruelle; Hausdorff dimension; hyperbolic set; fractal dimension; product structure}},
  language     = {{eng}},
  pages        = {{88--96}},
  publisher    = {{American Mathematical Society (AMS)}},
  series       = {{Electronic Research Announcements of the American Mathematical Society}},
  title        = {{Dimension product structure of hyperbolic sets}},
  url          = {{http://dx.doi.org/10.1090/S1079-6762-04-00133-7}},
  doi          = {{10.1090/S1079-6762-04-00133-7}},
  volume       = {{10}},
  year         = {{2004}},
}