A study of the dynamics of the family λ sinhmz z2m

Abstract EN

In this paper, the dynamical behavior of a family of non- critically finite transcendental mesomorphic function F λ (z) = λ (sinh m x) / (x 2m,), λ > 0 and m is an even natural number is described.

The Julia set of F λ (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 F λ (z) occurs at two critical parameter values λ = λ1, λ2, where λ1 = (X 1 2M + 1) / (SINH M X 1) and λ2 = (x 2m + 1) / sinh (m x 2) with x 1 and x 2 are the unique positive real roots of the equations tant x = mx / (2m-1) and then mx / (2m+1) respectively.