Iterates of meromorphic functions: I
- 1 June 1991
- journal article
- research article
- Published by Cambridge University Press (CUP) in Ergodic Theory and Dynamical Systems
- Vol. 11 (2) , 241-248
- https://doi.org/10.1017/s014338570000612x
Abstract
For functions meromorphic in the plane, apart from an exceptional case, the Julia set J is the closure of the set of all preimages of poles. The repelling periodic cycles are dense in J. In contrast with the case of transcendental entire functions, J may be a subset of a straight line and general classes of functions for which this is the case can be determined. J may also lie on a quasicircle through infinity which is not a straight line.Keywords
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