Iteration of a class of hyperbolic meromorphic functions |
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| Authors: | P. J. Rippon G. M. Stallard |
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| Affiliation: | Department of Pure Mathematics, The Open University, Walton Hall, Milton Keynes, MK7 6AA, England ; Department of Pure Mathematics, The Open University, Walton Hall, Milton Keynes, MK7 6AA, England |
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| Abstract: | We look at the class  which contains those transcendental meromorphic functions  for which the finite singularities of  are in a bounded set and prove that, if  belongs to  , then there are no components of the set of normality in which  as  . We then consider the class  which contains those functions  in  for which the forward orbits of the singularities of  stay away from the Julia set and show (a) that there is a bounded set containing the finite singularities of all the functions  and (b) that, for points in the Julia set of  , the derivatives  have exponential-type growth. This justifies the assertion that  is a class of hyperbolic functions. |
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