Chaotic behavior in real dynamics and singular values of family of generalized generating function of Apostol-Genocchi numbers
Volume 19, Issue 1, pp 41--50
http://dx.doi.org/10.22436/jmcs.019.01.06
Publication Date: March 06, 2019
Submission Date: November 19, 2018
Revision Date: February 14, 2019
Accteptance Date: February 20, 2019
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Authors
Mohammad Sajid
- College of Engineering, Qassim University, Buraidah, Al-Qassim, Saudi Arabia.
Abstract
Chaotic behavior in the real dynamics and singular values of a two-parameter family of generalized generating function of Apostol-Genocchi numbers, \(f_{\lambda,a}(z)=\lambda \frac{2z}{e^{az}+1}\),
\(\lambda, a\in \mathbb{R} \backslash \{0\}\), 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 \(a<0\).
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ISRP Style
Mohammad Sajid, Chaotic behavior in real dynamics and singular values of family of generalized generating function of Apostol-Genocchi numbers, Journal of Mathematics and Computer Science, 19 (2019), no. 1, 41--50
AMA Style
Sajid Mohammad, Chaotic behavior in real dynamics and singular values of family of generalized generating function of Apostol-Genocchi numbers. J Math Comput SCI-JM. (2019); 19(1):41--50
Chicago/Turabian Style
Sajid, Mohammad. "Chaotic behavior in real dynamics and singular values of family of generalized generating function of Apostol-Genocchi numbers." Journal of Mathematics and Computer Science, 19, no. 1 (2019): 41--50
Keywords
- Fixed points
- critical values
- singular values
- bifurcation
- chaos
- Lyapunov exponents
MSC
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