Random iteration of isometries in unbounded metric spaces
(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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/309750
- author
- Ambroladze, Amiran LU and Adahl, M
- organization
- publishing date
- 2003
- 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
- 2016-04-01 11:47:38
- date last changed
- 2022-01-26 18:19:00
@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}}, doi = {{10.1088/0951-7715/16/3/317}}, volume = {{16}}, year = {{2003}}, }