# Random iteration of isometries in unbounded metric spaces

Research output: Contribution to journal › Article

### Bibtex

@article{c71ddcebf36242ceb464f1426de16a50,

title = "Random iteration of isometries in unbounded metric spaces",

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 = "Amiran Ambroladze and M Adahl",

year = "2003",

doi = "10.1088/0951-7715/16/3/317",

language = "English",

volume = "16",

pages = "1107--1117",

journal = "Nonlinearity",

issn = "0951-7715",

publisher = "London Mathematical Society / IOP Science",

number = "3",

}