Chaos in Dynamics of a Family of Transcendental Meromorphic Functions

The characterization and properties of Julia sets of one parame-ter family of transcendental meromorphic functions ζλ(z) = λ z z+1e −z, λ> 0, z ∈ C is investigated in the present paper. It is found that bifurcations in the dynamics of ζλ(x), x ∈ R \ {−1}, occur at sev-eral parameter values and the dynamics of the family becomes chaotic when the parameter λ crosses certain values. The Lyapunov exponent of ζλ(x) for certain values of the parameter λ is computed for quan-tifying the chaos in its dynamics. The characterization of the Julia set of the function ζλ(z) as complement of the basin of attraction of an attracting real fixed point of ζλ(z) is found here and is applied to computationally simulate the images of the Julia sets of ζλ(z). Fur-ther, it is established that the Julia set of ζλ(z) for λ>