Baker domains of meromorphic functions

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

DOI: https://doi.org/10.1017/S0143385706000162

Abstract

Let $f$ be a transcendental meromorphic function and $U$ be an invariant Baker domain of $f$. We obtain a new estimate for the growth of the iterates of $f$ in $U$, and we use this estimate to improve an earlier result relating the geometric properties of $U$ and the proximity of $f$ in $U$ to the identity function. We illustrate the latter result by considering transcendental meromorphic functions $f$ of the form
$ f(z) = az + bz^ke^{-z}(1+o(1)) \; \mbox{ as } \Re (z) \rightarrow \infty, $
where $k \in \bf N$, $a > 1$ and $b > 0$, and we show that these functions have Baker domains which contain an unbounded set of critical points and an unbounded set of critical values.

Viewing alternatives

Metrics

Public Attention

Altmetrics from Altmetric

Number of Citations

Citations from Dimensions
No digital document available to download for this item

Item Actions

Export

About