Generalized chaotic maps and elementary functions between analysis and implementation

Nonlinear analysis and chaos have many applications in communications, cryptography, and many other fields. In this work, we aim to bridge the gap between mathematical analysis of generalized 1D discrete chaotic maps and their implementation on digital platforms. We propose several variations and generalizations on the logistic and tent maps and employ the power function z = x^y in a general map that could yield each of them and other new maps. Finite precision logistic map is studied explaining the impact of finitude on its properties. In addition, floating-point implementations of the power function are tested on the occurrence of special values of the operands.