We construct a transcendental entire function is an arbitrary prescribed function tending to infinity.

Entire functions of slow growth whose Julia set coincides with the plane

The dynamics of one parameter family of transcendental meromorphic functions , for λ > 0, a fix μ0>0 and , that have rational Schwarzian derivatives, is investigated in the present article. A computationally useful characterization of the Julia set of h λ(z) as complement of the basin of attraction of an attracting real fixed point of h λ(z) is proved and applied for computer generation of the images of the Julia sets of h λ(z). It is observed that for functions in our family bifurcations in the dynamics occur at three real parameter values, while for the family of functions  λ tan z investigated in [Devaney, R. L., and Keen, L., 1989, Dynamics of meromorphic maps: Maps with polynomial schwarzian derivative. Annales Scientifiques de l'Ecol1 Noemale Superieure, 22(4), 55–79.], bifurcation in the dynamics occurs at just one real parameter value. Further, it is found that explosion in the Julia sets of h λ(z) occurs for certain ranges of parameter values. Our results found here are compared with recent resul...

Dynamics of transcendental meromorphic functions (( )/( )) having rational Schwarzian derivatives

Real fixed points and dynamics of one parameter family of function

Singular values of two-parameter families λ((bz − 1)/z)μ and λ(z/(bz − 1))η

In the present paper, the singular values of one parameter family of entire functions f ( z) = ( e z 1 z ) m and f (0) = , m 2 Nnf 0 g , 2 Rnf 0 g , z 2 C is investigated. It is shown that all the critical values of f ( z) lie in the left half plane. It is also found that the function

Singular Values of One Parameter Family

/pdf/julia-set-of-the-function-z-exp-z-mu-3iip7k0xng.pdf

Tadashi Kuroda

Papers

Julia set of the function $z\exp(z+\mu)$