Skip to main content Accessibility help
×
Home

Hyperbolic Metric and Multiply Connected Wandering Domains of Meromorphic Functions

  • Jian-Hua Zheng (a1)

Abstract

In this paper, in terms of the hyperbolic metric, we give a condition under which the image of a hyperbolic domain of an analytic function contains a round annulus centred at the origin. From this, we establish results on the multiply connected wandering domains of a meromorphic function that contain large round annuli centred at the origin. We thereby successfully extend the results of transcendental meromorphic functions with finitely many poles to those with infinitely many poles.

Copyright

References

Hide All
1. Baker, I. N., The domains of normality of an entire function, Annales Acad. Sci. Fenn. Math. 1 (1975), 277283.
2. Baker, I. N., Kotus, J. and , Y., Iterates of meromorphic functions III: examples of wandering domains, J. Lond. Math. Soc. 42(2) (1990), 267278.
3. Beardon, A. F., Iteration of rational functions (Springer, 1991).
4. Beardon, A. F. and Pommerenke, Ch., The Poincaré metric of plane domains, J. Lond. Math. Soc. 18(2) (1978), 475483.
5. Bergweiler, W., Iteration of meromorphic functions, Bull. Am. Math. Soc. 29 (1993), 151188.
6. Bergweiler, W. and Terglane, N., Weakly repelling fixpoints and the connectivity of wandering domains, Trans. Am. Math. Soc. 348 (1996), 112.
7. Bergweiler, W., Rippon, P. J. and Stallard, G. M., Multiply connected wandering domains of entire functions, Proc. Lond. Math. Soc. 107 (2013), 12611301.
8. Carleson, L. and Gamelin, T. W., Complex dynamics (Springer, 1993).
9. Dominguez, P., Dynamics of transcendental meromorphic functions, Annales Acad. Sci. Fenn. Math. 23 (1998), 225250.
10. Milnor, J., Dynamics in one complex variable: introductory lectures, Stony Brook Institute for Mathematical Sciences, Preprint (arXiv:math/9201272 [math.DS]; 1990).
11. Rippon, P. J. and Stallard, G. M., Slow escaping points of meromorphic functions, Trans. Am. Math. Soc. 363 (2011), 41714201.
12. Rudin, W., Real and complex analysis (McGraw-Hill, 1986).
13. Whittington, J. E., On the fixpoints of entire functions, Proc. Lond. Math. Soc. 17 (1967), 530546.
14. Zheng, J.-H., On non-existence of unbounded domains of normality of meromorphic functions, J. Math. Analysis Applic. 264 (2001), 479494.
15. Zheng, J.-H., Uniformly perfect sets and distortion of holomorphic functions, Nagoya Math. J. 164 (2001), 1733.
16. Zheng, J.-H., Dynamics of transcendental meromorphic functions (in Chinese) (Tsinghua University Press, 2004).
17. Zheng, J.-H., On multiply-connected Fatou components in iteration of meromorphic functions, J. Math. Analysis Applic. 313 (2006), 2437.
18. Zheng, J.-H., Value distribution of meromorphic functions (Tsinghua University Press/Springer, 2010).
19. Zheng, J.-H., Domain constants and their applications in dynamics of meromorphic functions, J. Jiangxi Normal Univ. (Nat. Sci. Edn) 34(5) (2010), 17.

Keywords

MSC classification

Hyperbolic Metric and Multiply Connected Wandering Domains of Meromorphic Functions

  • Jian-Hua Zheng (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed