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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

MSC:
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
Keywords:
iterate; Julia set
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