Random iteration of isometries in unbounded metric spaces
(2003) In Nonlinearity 16(3). p.11071117 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
 09517715
 DOI
 10.1088/09517715/16/3/317
 language
 English
 LU publication?
 yes
 id
 c71ddcebf36242ceb464f1426de16a50 (old id 309750)
 date added to LUP
 20160401 11:47:38
 date last changed
 20210217 04:59:10
@article{c71ddcebf36242ceb464f1426de16a50, 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 = {09517715}, language = {eng}, number = {3}, pages = {11071117}, publisher = {London Mathematical Society / IOP Science}, series = {Nonlinearity}, title = {Random iteration of isometries in unbounded metric spaces}, url = {http://dx.doi.org/10.1088/09517715/16/3/317}, doi = {10.1088/09517715/16/3/317}, volume = {16}, year = {2003}, }