APM  Vol.4 No.5 , May 2014
Finite Type Transcendental Entire Functions Whose Buried Points Set Contains Unbounded Positive Real Interval
Author(s) Feng Guo*
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.


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.

 
 
Top