Dimension product structure of hyperbolic sets
(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:
https://lup.lub.lu.se/record/268192
- author
- Hasselblatt, B and Schmeling, Jörg LU
- organization
- publishing date
- 2004
- 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}}, }