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contributor.authorPrasad, M Guru Prem-
contributor.authorNayak, T-
date.accessioned2009-07-31T10:30:07Z-
date.available2009-07-31T10:30:07Z-
date.issued2007-09-
identifier.citationDiscrete and Continuous Dynamical Systems, Vol 19, Number 1, September 2007, pp. 121–138en
identifier.urihttp://hdl.handle.net/2080/975-
description.abstractAbstract. 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.en
format.extent243756 bytes-
format.mimetypeapplication/pdf-
language.isoen-
publisherAmerican Institute of Mathematical Sciences.en
titleDYNAMICS OF {λ tanh(ez) : λ ∈ R \ {0}}en
typeArticleen
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