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Iterates of meromorphic functions III: Preperiodic domains

  • I. N. Baker (a1), J. Kotus (a2) and Lü Yinian (a3)

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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