TY - JOUR AU - Sajid, Mohammad PY - 2019 TI - Chaotic behavior in real dynamics and singular values of family of generalized generating function of Apostol-Genocchi numbers JO - Journal of Mathematics and Computer Science SP - 41--50 VL - 19 IS - 1 AB - Chaotic behavior in the real dynamics and singular values of a two-parameter family of generalized generating function of Apostol-Genocchi numbers, \(f_{\lambda,a}(z)=\lambda \frac{2z}{e^{az}+1}\), \(\lambda, a\in \mathbb{R} \backslash \{0\}\), are investigated. The real fixed points of \(f_{\lambda,a}(z)\) and their nature are studied. It is seen that bifurcation and chaos occur in the real dynamics of \(f_{\lambda,a}(z)\). It is also found that the function \(f_{\lambda,a}(z)\) has infinitely many singular values for \(a>0\) and \(a<0\). The critical values of \(f_{\lambda,a}(z)\) lie inside the open disk, the annulus and exterior of the open disk at center origin for \(a>0\) and \(a<0\). SN - ISSN 2008-949X UR - http://dx.doi.org/10.22436/jmcs.019.01.06 DO - 10.22436/jmcs.019.01.06 ID - Sajid2019 ER -