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Rippon, P.J.
(2006).
DOI: https://doi.org/10.1017/S0143385706000162
Abstract
Let be a transcendental meromorphic function and
be an invariant Baker domain of
. We obtain a new estimate for the growth of the iterates of
in
, and we use this estimate to improve an earlier result relating the geometric properties of
and the proximity of
in
to the identity function. We illustrate the latter result by considering transcendental meromorphic functions
of the form
where ,
and
, and we show that these functions have Baker domains which contain an unbounded set of critical points and an unbounded set of critical values.