A STUDY OF THE DYNAMICS OF THE FAMILY λ - AL-Husseiny, Hassan (Iraqi Journal of Science, 2024)
In this paper, the dynamical behavior of a family of non- critically finitetranscendental meromorphic function fλ (z) =λ mmxx2sinh , λ >0 and m is an evennatural number is described. The Julia set of fλ (z) , as the closure of the set ofpoints with orbits escaping to infinity under iteration, is obtained. It is observed that,bifurcation in the dynamics of fλ (z) occurs at two critical parameter values λ = λ1,λ2, where λ1 =12 11sinh xxmm+and λ2 =22 12sinh xxmm+with x1 and x2 are the uniquepositive real roots of the equations tanh x =2m−1mx and tanh x =2m +1mx respectively.