ISSN: 1813-0410

Author : A. Ahmed, Buthainah

Dynamics of meromorphic family λ with non-critically finite

Hassan Fadhil Al-Husseiny; Buthainah A. Ahmed

journal of kerbala university, Volume 6, Issue 2, Pages 464-475

In this paper, a one-parameter family Ƭ = { = λf(z), λ > 0} with f(z) = , m is Natural number is considered, it is obtain that family has non-critically finite. The dynamics of the meromorphic transcendental functions fλ  Ƭ is studied in detailed. It was found that the bifurcations in the dynamics of the functions fλ(x) occur at parameter values λ1 and λ2 where λi = Φ (xi), (i = 1, 2), and Φ(x) = with x1 is the solution of the equation coth x = while x2 is the unique positive roots of the equation Φ′ (x) = 0.