# Baker domains of meromorphic functions

Rippon, P.J. (2006). Baker domains of meromorphic functions. Ergodic Theory and Dynamical Systems, 26(4) pp. 1225–1233.

## 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.

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