DSpace@nitr >
National Institue of Technology- Rourkela >
Journal Articles >

Please use this identifier to cite or link to this item: 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

Files in This Item:

File Description SizeFormat
t.nayak1.pdf238KbAdobe PDFView/Open

Show full item record

All items in DSpace are protected by copyright, with all rights reserved.

 

Powered by DSpace Feedback