Singularities of meromorphic functions with Baker domains
We show that if $f$ is a transcendental meromorphic function with a finite number of poles and $f$ has a cycle of Baker domains of period $p$, then there exist $C > 1$ and $r_0>0$ such that $\bigg\{z:\frac1C r\lt |z|\lt Cr\bigg\}\cap \mbox{sing} (f^{-p})\ne\varnothing,{\for}r\ge r_0.$ We also...
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| Veröffentlicht in: | Mathematical proceedings of the Cambridge Philosophical Society 2006-09, Vol.141 (2), p.371-382 |
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| container_title | Mathematical proceedings of the Cambridge Philosophical Society |
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| creator | RIPPON, P. J. STALLARD, G. M. |
| description | We show that if $f$ is a transcendental meromorphic function with a finite number of poles and $f$ has a cycle of Baker domains of period $p$, then there exist $C > 1$ and $r_0>0$ such that $\bigg\{z:\frac1C r\lt |z|\lt Cr\bigg\}\cap \mbox{sing} (f^{-p})\ne\varnothing,{\for}r\ge r_0.$ We also give examples to show that this result fails for transcendental meromorphic functions with infinitely many poles. |
| doi_str_mv | 10.1017/S0305004106009315 |
| format | Article |
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| title | Singularities of meromorphic functions with Baker domains |
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