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Borel directions and iterated orbits of meromorphic functions

Published online by Cambridge University Press:  17 April 2009

Jianyong Qiao
Jianyong Qiao
Affiliation:
Center for Mathematics, China University of Mining and Technology (Beijing), Xueyuan Road, Ding 11, Beijing 100083, Peoples Republic of China, e-mail: [email protected] Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, Peoples Republic of China
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Abstract

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For transcendental meromorphic functions of finite order, we prove that there exist iterated orbits which tend to the Borel directions. This gives a relation between the value distribution theory and the iteration theory of meromorphic functions.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 61 , Issue 1 , February 2000 , pp. 1 - 9
Copyright
Copyright © Australian Mathematical Society 2000

References

REFERENCES

[1]Baker, I.N., ‘Infinite limits in the iteration of entire functions’, Ergodic Theory Dynamical Systems 8 (1988), 503–507.CrossRefGoogle Scholar
[2]Bergweiler, W., ‘Iteration of meromorphic functions’, Bull. Amer. Math. Soc. 29 (1993), 151–188.CrossRefGoogle Scholar
[3]Eremenko, A.E., ‘On the iteration of entire functions’, in Dynamical System and Ergodic Theory, Banach Center Publications 23 (Polish Scientific Publishers, Warsaw, 1989), pp. 339–345.Google Scholar
[4]Hayman, W.K., ‘Angular value distribution of power series with gaps’, Proc. London Math. Soc. 24 (1972), 590–624.CrossRefGoogle Scholar
[5]Yang, L., Value distribution theory (Springer-Verlag, Berlin, Heidelberg, New York; Science Press, Beijing, 1993).Google Scholar