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http://hdl.handle.net/2080/975
Title: | DYNAMICS OF {λ tanh(ez) : λ ∈ R \ {0}} |
Authors: | Prasad, M Guru Prem Nayak, T |
Issue Date: | Sep-2007 |
Publisher: | American Institute of Mathematical Sciences. |
Citation: | Discrete and Continuous Dynamical Systems, Vol 19, Number 1, September 2007, pp. 121–138 |
Abstract: | Abstract. In this paper, the dynamics of transcendental meromorphic func- tions in the one-parameter family M= {f(z) = f(z) : f(z) = tanh(ez) for z 2 C and 2 R \ {0} } is studied. We prove that there exists a parameter value −3.2946 such that the Fatou set of f(z) is a basin of attraction of a real fixed point for > and, is a parabolic basin corresponding to a real fixed point for = . It is a basin of attraction or a parabolic basin corresponding to a real periodic point of prime period 2 for < . If > , it is proved that the Fatou set of f is connected and, is infinitely connected. Consequently, the singleton components are dense in the Julia set of f for > . If , it is proved that the Fatou set of f contains infinitely many pre-periodic components and each component of the Fatou set of f is simply connected. Finally, it is proved that the Lebesgue measure of the Julia set of f for 2 R \ {0} is zero. |
URI: | http://hdl.handle.net/2080/975 |
Appears in Collections: | Journal Articles |
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File | Description | Size | Format | |
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t.nayak1.pdf | 238.04 kB | Adobe PDF | View/Open |
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