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Iterates of meromorphic functions. I. (English) Zbl 0711.30024
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.
Reviewer: I.N.Baker

30D05 Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable
30D30 Meromorphic functions of one complex variable (general theory)
37B99 Topological dynamics
iterate; Julia set
Full Text: DOI
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