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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
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
2008-01-24 16:25:44
date last changed
2017-03-16 14:24:01
@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},
  keyword      = {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},
  volume       = {32},
  year         = {2009},
}