Abstract
Chaotic behavior in the real dynamics and singular values of a two-parameter family of generalized generating function of Apostol-Genocchi numbers, f(lambda, a)(z) = lambda(2z)(e alpha z+1) , lambda, alpha subset of IR\{0}, are investigated. The real fixed points of f(lambda, alpha)(z) and their nature are studied. It is seen that bifurcation and chaos occur in the real dynamics of f(lambda, alpha)(z). It is also found that the function f(lambda, alpha)(z) has infinitely many singular values for alpha > 0 and alpha < 0. The critical values of f(lambda, alpha)(z) lie inside the open disk, the annulus and exterior of the open disk at center origin for alpha > 0 and alpha < 0.