Author/Authors :
AL-Husseiny, Hassan Fadhil University of Baghdad - College of Science - Department of Mathematics, Iraq
Abstract :
In this paper, the dynamical behavior of a family of non- critically finite sinh m transcendental meromorphic function f x A(z) =1 —— , 1 0 and m is an even natural number is described. The Julia set of fx (z), as the closure of the set of points with orbits escaping to infinity under iteration, is obtained. It is observed that, bifurcation in the dynamics of fx (z) occurs at two critical parameter values 1 = 11,2m+112, where 11 =sinhm x1and 12 =x 2m+ 1sinh m x2with x1 and x2 are the uniquepositive real roots of the equations tanh x = mx and. t.a nh. x = mx2m - 1 2m +1respectively
