Complex squaring map Polynomial, Complex number, Argument (complex analysis), Orbit (dynamics), Dyadic transformation, Radix, Logistic function, List of chaotic maps

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, the complex squaring map, a polynomial mapping of degree two, is a simple and accessible demonstration of chaos in dynamical systems. It can be constructed by performing the following steps: Choose any complex number on the unit circle whose argument (complex angle) is not a rational fraction of ?, Repeatedly square that number. This repetition (iteration) produces a sequence of complex numbers that can be described by their complex angle alone. Any choice of starting angle that satisfies above will produce an extremely complicated sequence of angles, that belies the simplicity of the steps. In fact, it can be shown that the sequence will be chaotic, i.e. it is sensitive to the detailed choice of starting angle. Sprache: Englisch Gewicht in Gramm: 119.