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Random iteration of isometries in unbounded metric spaces

Ambroladze, Amiran LU and Adahl, M (2003) In Nonlinearity 16(3). p.1107-1117
Abstract
We consider an iterated function system (with probabilities) of isometrics on an unbounded metric space (X, d). Under suitable conditions it is proved that the random orbit {Z(n)}(ngreater than or equal to0) of the iterations corresponding to an initial point Z(0) is an element of X 'escapes to infinity' in the sense that P(Z(n) is an element of K) --> 0, as n --> infinity for every bounded set K subset of X. As an application we prove the corresponding result in the Euclidean and hyperbolic spaces under the condition that the isometries do not have a common fixed point.
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Nonlinearity
volume
16
issue
3
pages
1107 - 1117
publisher
London Mathematical Society / IOP Science
external identifiers
  • wos:000183174000018
  • scopus:0242276993
ISSN
0951-7715
DOI
10.1088/0951-7715/16/3/317
language
English
LU publication?
yes
id
c71ddceb-f362-42ce-b464-f1426de16a50 (old id 309750)
date added to LUP
2007-08-22 10:40:18
date last changed
2018-01-07 05:23:09
@article{c71ddceb-f362-42ce-b464-f1426de16a50,
  abstract     = {We consider an iterated function system (with probabilities) of isometrics on an unbounded metric space (X, d). Under suitable conditions it is proved that the random orbit {Z(n)}(ngreater than or equal to0) of the iterations corresponding to an initial point Z(0) is an element of X 'escapes to infinity' in the sense that P(Z(n) is an element of K) --> 0, as n --> infinity for every bounded set K subset of X. As an application we prove the corresponding result in the Euclidean and hyperbolic spaces under the condition that the isometries do not have a common fixed point.},
  author       = {Ambroladze, Amiran and Adahl, M},
  issn         = {0951-7715},
  language     = {eng},
  number       = {3},
  pages        = {1107--1117},
  publisher    = {London Mathematical Society / IOP Science},
  series       = {Nonlinearity},
  title        = {Random iteration of isometries in unbounded metric spaces},
  url          = {http://dx.doi.org/10.1088/0951-7715/16/3/317},
  volume       = {16},
  year         = {2003},
}