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- W2017221818 abstract "Let E denote the class of all transcendental entire functions f(z)=∑n=0∞anzn for z∈C and an⩾0 for all n⩾0 such that f(x)>0 for x<0 and the set of all (finite) singular values of f forms a bounded subset of R. For each f∈E, one parameter family S={fλ≡λf:λ>0} is considered. In this paper, we mainly study the dynamics of functions in the one parameter family S. 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 S 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 F(fλ) of fλ is connected whenever it is an attracting basin and the immediate basin contains all the finite singular values of fλ. Finally, a number of interesting examples of entire transcendental functions from the class E are discussed." @default.
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- W2017221818 date "2007-05-01" @default.
- W2017221818 modified "2023-09-25" @default.
- W2017221818 title "Dynamics of certain class of critically bounded entire transcendental functions" @default.
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- W2017221818 doi "https://doi.org/10.1016/j.jmaa.2006.06.095" @default.
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