Julia Sets of Joukowski-Exponential Maps

Bifurcation and Chaos in Real Dynamics of a Two-Parameter Family Arising from Generating Function of Generalized Apostol-Type Polynomials

“…Such investigations are interesting for the description of Julia sets, Fatou sets and other properties in the complex dynamics; see for instance [20][21][22][23][24][25][26]. Moreover, the study of real dynamics has attracted much interest from researchers due to the fast-growing availability of computer software for both simulation and graphics.…”

Singular values of two-parameter families λ((bz − 1)/z)μ and λ(z/(bz − 1))η

“…This exponential family is simpler than other families which have more than one or infinitely many singular values. Some dynamical properties of such types of families of functions including exponential map were studied in [7][8][9][10][11]. Often these investigations are very applicable for studying of iterative methods associate to entire and meromorphic transcendental functions which have either critical values or asymptotic values, or both.…”

“…Often these investigations are very applicable for studying of iterative methods associate to entire and meromorphic transcendental functions which have either critical values or asymptotic values, or both. Enormously, singular values are useful in the dynamics of entire and meromorphic transcendental functions for describing the Julia sets and the Fatou sets [8][9][10][11][12].…”

Singular Values Of One Parameter Family \lambda\frac{b^2-1}{z}

“…The dynamics of one parameter family z e  , that has only one singular value, is studied in detail [1,2,3]. This exponential family is simpler than other families of functions which involving exponential maps [4,5,6,7] and having more than one or infinitely many singular values. The singular values and dynamics of family 1 z e z   are studied by Kapoor and Prasad [8].…”