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The Hausdorff dimension of the set of dissipative points for a Cantor-like model set of singly cusped parabolic dynamics

Schmeling, Jörg LU and Stratmann, Bernd (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.
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author
and
organization
publishing date
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}},
}