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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.

    Levin, Genadi and Światek, Grzegorz 2005. Dynamics and Universality of Unimodal Mappings with Infinite Criticality. Communications in Mathematical Physics, Vol. 258, Issue. 1, p. 103.

    Maneeruk, Keaitsuda and Niamsup, Piyapong 2005. Dynamics of composite functions meromorphic outside a small set. Journal of Mathematical Analysis and Applications, Vol. 306, Issue. 1, p. 218.


Dynamics of functions meromorphic outside a small set

  • I. N. BAKER (a1), P. DOMÍNGUEZ (a2) and M. E. HERRING (a1)
  • DOI:
  • Published online: 01 June 2001

The theory of Fatou and Julia is extended to include the dynamics of functions f which are meromorphic in \widehat{\mathbb{C}} outside a totally disconnected compact set E(f) at whose points the cluster set of f is \widehat{\mathbb{C}}. The Julia set is defined not only by the standard approach but is also characterized in terms of the set of points whose orbits approach a point of E(f). For the subclass where E(f) has a complement of class OAD and the inverse of f has a finite set of singular points it is shown that neither wandering components nor Baker domains occur in F(f)>. As an application, functions of a certain general class are shown to have a totally disconnected Julia set.

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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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