The Hausdorff dimension of the set of dissipative points for a Cantor-like model set of singly cusped parabolic dynamics
(2009) In Kodai Mathematical Journal 32(2). p.179-196- Abstract
- In this paper we introduce and study a certain intricate Cantor-like set C contained in unit interval. Our main result is to show that the set C itself, as well as the set of dissipative points within C, both have Hausdorff dimension equal to 1. The proof uses the transience of a certain non-symmetric Cauchy-type random walk.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/945832
- author
- Schmeling, Jörg LU and Stratmann, Bernd
- organization
- publishing date
- 2009
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Hausdorff dimension, Fractal geometry, Cauchy random walks, Kleinian, groups
- in
- Kodai Mathematical Journal
- volume
- 32
- issue
- 2
- pages
- 179 - 196
- publisher
- Kinokuniya Co Ltd
- external identifiers
-
- wos:000269241400001
- scopus:77956462611
- ISSN
- 0386-5991
- DOI
- 10.2996/kmj/1245982902
- language
- English
- LU publication?
- yes
- id
- 5e2be8d6-ac5f-46bc-8d6c-55b8a0272ce0 (old id 945832)
- date added to LUP
- 2016-04-01 13:27:47
- date last changed
- 2022-01-27 19:19:46
@article{5e2be8d6-ac5f-46bc-8d6c-55b8a0272ce0, abstract = {{In this paper we introduce and study a certain intricate Cantor-like set C contained in unit interval. Our main result is to show that the set C itself, as well as the set of dissipative points within C, both have Hausdorff dimension equal to 1. The proof uses the transience of a certain non-symmetric Cauchy-type random walk.}}, author = {{Schmeling, Jörg and Stratmann, Bernd}}, issn = {{0386-5991}}, keywords = {{Hausdorff dimension; Fractal geometry; Cauchy random walks; Kleinian; groups}}, language = {{eng}}, number = {{2}}, pages = {{179--196}}, publisher = {{Kinokuniya Co Ltd}}, series = {{Kodai Mathematical Journal}}, title = {{The Hausdorff dimension of the set of dissipative points for a Cantor-like model set of singly cusped parabolic dynamics}}, url = {{http://dx.doi.org/10.2996/kmj/1245982902}}, doi = {{10.2996/kmj/1245982902}}, volume = {{32}}, year = {{2009}}, }