Random iteration of isometries in unbounded metric spaces

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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.

Detaljer

Författare
  • Amiran Ambroladze
  • M Adahl
Enheter & grupper
Forskningsområden

Ämnesklassifikation (UKÄ) – OBLIGATORISK

  • Matematik
Originalspråkengelska
Sidor (från-till)1107-1117
TidskriftNonlinearity
Volym16
Utgåva nummer3
StatusPublished - 2003
PublikationskategoriForskning
Peer review utfördJa