Share This Article:

Finite Type Transcendental Entire Functions Whose Buried Points Set Contains Unbounded Positive Real Interval

Abstract Full-Text HTML Download Download as PDF (Size:259KB) PP. 209-212
DOI: 10.4236/apm.2014.45027    5,497 Downloads   6,336 Views  
Author(s)    Leave a comment

ABSTRACT

Let fμ(z)=z·ep(z)+μ with p(z) being real coefficient polynomial and it's leading coefficient be positive, μ∈R+, when p(z) and μ satisfy two certain conditions, buried point set of fμ(z) contains unbounded positive real interval.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Guo, F. (2014) Finite Type Transcendental Entire Functions Whose Buried Points Set Contains Unbounded Positive Real Interval. Advances in Pure Mathematics, 4, 209-212. doi: 10.4236/apm.2014.45027.

References

[1] Eremenko, A.E. and Lyubich, M.Yu (.1990) The Dynamics of Analytic Transformations. Leningrad Mathematical Journal, 1, 563.
[2] Beardon, A.F. (1991) Iteration of Rational Functions. Springer, Berlin.
http://dx.doi.org/10.1007/978-1-4612-4422-6
[3] Milnor, J. (2006) Dynamics in One Complex Variable. 3rd Edition, Princeton University Press, Princeton and Oxford.
[4] Qiao, J. (2010) Complex Dynamics on Renormalization Transformations. Science Press, Beijing. (in Chinese)
[5] Morosawa, S., Nishimura, Y., Taniguchi, M. and Ueda, T. (2000) Holomorphic Dynamics, Cambridge University Press.
[6] Baker, I.N. (1970) Limit Functions and Sets of Non-Normality in Iteration Theory. Annales Academiae Scientiarum Fennicae. Series A 1, Mathematica, 467, 1-11.
[7] Jang, C.M. (1992) Julia Set of the Function z exp(z + μ). Tohoku Mathematical Journal, 44, 271-277.
[8] Qiao, J. (1994) The Set of the Mapping z exp(z + μ). Chinese Science Bulletin, 39, 529.
[9] Qiao, J. (1995) The Buried Points on the Julia Sets of Rational and Entire Functions. Science in China Series A, 38, 1409-1419.

  
comments powered by Disqus

Copyright © 2019 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.