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http://hdl.handle.net/2080/976
Title: | Iteration of Certain Meromorphic Functions with Unbounded Singular Values |
Authors: | Nayak, T Prasad, M Guru Prem |
Issue Date: | Jul-2009 |
Publisher: | Cambridge University Press |
Citation: | Ergodic Theory and Dynamical Systems, 21 July 2009, Pages 1-15 |
Abstract: | Let MD f f .z/ D .zm=sinhm z/ for z 2 C j either m or m=2 is an odd natural numberg. For each f 2M, the set of singularities of the inverse function of f is an unbounded subset of the real line R. In this paper, the iteration of functions in oneparameter family S D f f.z/ D f .z/ j 2 R n f0gg is investigated for each f 2M. It is shown that, for each f 2M, there is a critical parameter > 0 depending on f such that a period-doubling bifurcation occurs in the dynamics of functions f in S when the parameter jj passes through . The non-existence of Baker domains and wandering domains in the Fatou set of f is proved. Further, it is shown that the Fatou set of f is infinitely connected for 0 < jj whereas for jj , the Fatou set of f consists of infinitely many components and each component is simply connected. |
URI: | http://dx.doi.org/10.1109/IADCC.2009.4809075 http://hdl.handle.net/2080/976 |
Appears in Collections: | Journal Articles |
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t.nayak.pdf | 181.54 kB | Adobe PDF | View/Open |
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