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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.
Please use this url to cite or link to this publication:
author
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
Amer Mathematical Soc
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
2007-10-29 14:57:11
date last changed
2017-03-16 14:24:02
@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},
  keyword      = {Lipschitz continuity,holonomies,conjecture,Eckmann-Ruelle,Hausdorff dimension,hyperbolic set,fractal dimension,product structure},
  language     = {eng},
  pages        = {88--96},
  publisher    = {Amer Mathematical Soc},
  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},
  volume       = {10},
  year         = {2004},
}