# Random iteration of isometries in unbounded metric spaces

Forskningsoutput: TidskriftsbidragArtikel i vetenskaplig tidskrift

### Standard

Random iteration of isometries in unbounded metric spaces. / Ambroladze, Amiran; Adahl, M.

I: Nonlinearity, Vol. 16, Nr. 3, 2003, s. 1107-1117.

Forskningsoutput: TidskriftsbidragArtikel i vetenskaplig tidskrift

### Author

Ambroladze, Amiran ; Adahl, M. / Random iteration of isometries in unbounded metric spaces. I: Nonlinearity. 2003 ; Vol. 16, Nr. 3. s. 1107-1117.

### RIS

TY - JOUR

T1 - Random iteration of isometries in unbounded metric spaces

PY - 2003

Y1 - 2003

N2 - 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.

AB - 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.

U2 - 10.1088/0951-7715/16/3/317

DO - 10.1088/0951-7715/16/3/317

M3 - Article

VL - 16

SP - 1107

EP - 1117

JO - Nonlinearity

JF - Nonlinearity

SN - 0951-7715

IS - 3

ER -