Fixed points and dynamics on generating function of Genocchi numbers

Recently, there have been many works related with dynamics of various functions. In this paper, singular values and fixed points of generating function of Genocchi numbers, gλ(z) = λ 2z/ez+1, λ(Ɛ R) 1, are investigated. It is shown that the function gλ(z) has in nitely many singular values and its critical values lie in the left half plane and one point on the real axis in the right half plane. Further, the real xed points of g (z) and their nature are determined. Finally, we provide numerical evidence of the existence of chaotic phenomena by illustrating bifurcation diagrams of system and by calculating the Lyapunov exponent. c 2016 All rights reserved.