This paper studies the asymptotic properties of the random iterations of both the form G. = f1 o f2 o''' o fn and the form Fn= fn o fn-1 o''' o f1, where {fn} H(Ω,Ω) and Ω C ￣N is a boun...This paper studies the asymptotic properties of the random iterations of both the form G. = f1 o f2 o''' o fn and the form Fn= fn o fn-1 o''' o f1, where {fn} H(Ω,Ω) and Ω C ￣N is a bounded domain. It is found that, under some conditions, Gn or Fn tends to a point in Ω as Ω→ ∞. Some examples are also given to show that the conditions that we have given can not be dropped in general. Moreover, a complete description is given for Fn or Gn to tend to a point in Ω under the condition fn→ f.展开更多
文摘This paper studies the asymptotic properties of the random iterations of both the form G. = f1 o f2 o''' o fn and the form Fn= fn o fn-1 o''' o f1, where {fn} H(Ω,Ω) and Ω C ￣N is a bounded domain. It is found that, under some conditions, Gn or Fn tends to a point in Ω as Ω→ ∞. Some examples are also given to show that the conditions that we have given can not be dropped in general. Moreover, a complete description is given for Fn or Gn to tend to a point in Ω under the condition fn→ f.
