Random iteration of isometries in unbounded metric spaces

Research output: Contribution to journalArticle

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.

Details

Authors
  • Amiran Ambroladze
  • M Adahl
Organisations
Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Mathematics
Original languageEnglish
Pages (from-to)1107-1117
JournalNonlinearity
Volume16
Issue number3
Publication statusPublished - 2003
Publication categoryResearch
Peer-reviewedYes