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    Gao, Junyang and Liu, Gang 2014. On Connectivity of Fatou Components concerning a Family of Rational Maps. Abstract and Applied Analysis, Vol. 2014, p. 1.

    Domínguez, Patricia and Hernández, Iván 2013. Conditions Where the Chaotic Set Has a Non-Empty Residual Julia Set for Two Classes of Meromorphic Functions. Applied Mathematics, Vol. 04, Issue. 11, p. 18.

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    Baker, I. N. Kotus, J. and Yinian, Lü 1991. Iterates of meromorphic functions III: Preperiodic domains. Ergodic Theory and Dynamical Systems, Vol. 11, Issue. 04,

  • Ergodic Theory and Dynamical Systems, Volume 11, Issue 4
  • December 1991, pp. 603-618

Iterates of meromorphic functions III: Preperiodic domains

  • I. N. Baker (a1), J. Kotus (a2) and Lü Yinian (a3)
  • DOI:
  • Published online: 01 September 2008

The paper discusses the connectivity of periodic and preperiodic domains in the stable set in the iteration of a meromorphic function. The connectivity of an invariant component has one of the values 1, 2, ∞. Examples are constructed to show that the connectivity of a preperiodic component may take any value.

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[5]I. N. Baker , J. Kotus & Yinian . Iterates of meromorphic functions I. Ergod. Th. & Dynam. Sys. 11 (2) (1991), 241248.

[9]I. P. Cornfeld , S. V. Fomin & Ya. G. Sinai . Ergodic Theory. Springer, New York, 1982.

[16]P. Fatou . Sur l'itération des fonctions transcendantes entières. Acta Math. 47 (1926), 337370.

[18]M. R. Herman . Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations. Publ. Math. I.H.E.S. 49 (1979), 5233.

[20]L. Keen . Dynamics of Holomorphic Self-maps of CK, Holomorphic Functions and Moduli I. MSRI Publications 10. Springer, New York, 1988.

[22]O. Lehto . Univalent Functions and Teichmüller Spaces. Springer, New York, 1987.

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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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