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  • Cited by 2
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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Lifang, Xu and Huanhuan, Yang 2012. On the generalizations of Denjoy-Wolff theorem. Acta Mathematica Scientia, Vol. 32, Issue. 4, p. 1333.

    Dutkay, Dorin Ervin and Jorgensen, Palle E.T. 2007. Fourier frequencies in affine iterated function systems. Journal of Functional Analysis, Vol. 247, Issue. 1, p. 110.


Random iteration of analytic maps

  • A. F. BEARDON (a1), T. K. CARNE (a1), D. MINDA (a2) and T. W. NG (a3)
  • DOI:
  • Published online: 01 May 2004

We consider analytic maps $f_j:D\to D$ of a domain D into itself and ask when does the sequence $f_1\circ\dotsb\circ f_n$ converge locally uniformly on D to a constant. In the case of one complex variable, we are able to show that this is so if there is a sequence $\{w_1,w_2,\dotsc\}$ in D whose values are not taken by any fj in D, and which is homogeneous in the sense that it comes within a fixed hyperbolic distance of any point of D. The situation for several complex variables is also discussed.

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Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
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