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Please use this identifier to cite or link to this item: http://hdl.handle.net/2080/648

Title: Dynamics of certain class of critically bounded entire transcendental functions
Authors: Guru Prem Prasad, M
Nayak, T
Keywords: Bifurcation
Choatic burst
Julia Sets
Fatou Sets
Issue Date: 2007
Publisher: Elsevier
Citation: Journal of Mathematical Analysis and Applications, Vol 329, Iss 2, P 1446-1459
Abstract: Let E denote the class of all transcendental entire functions Click to view the MathML source for Click to view the MathML source and angreater-or-equal, slanted0 for all ngreater-or-equal, slanted0 such that f(x)>0 for x<0 and the set of all (finite) singular values of f forms a bounded subset of Click to view the MathML source. For each fset membership, variantE, one parameter family Click to view the MathML source is considered. In this paper, we mainly study the dynamics of functions in the one parameter family Click to view the MathML source. If f(0)≠0, we show that there exists a positive real number λ* (depending on f) such that the bifurcation and the chaotic burst occur in the dynamics of functions in the one parameter family Click to view the MathML source at the parameter value λ=λ*. If f(0)=0, it is proved that the Julia set of fλ is equal to the complement of the basin of attraction of the super attracting fixed point 0 for all λ>0. It is also shown that the Fatou set Clic...
Description: Copyright for the paper belongs to Elsevier
URI: http://dx.doi.org/10.1016/j.jmaa.2006.06.095
http://hdl.handle.net/2080/648
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