About: Complex squaring map

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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: 1. * Choose any complex number on the unit circle whose argument (angle) is not a rational multiple of π, 2. * Repeatedly square that number.

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  • 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: 1. * Choose any complex number on the unit circle whose argument (angle) is not a rational multiple of π, 2. * Repeatedly square that number. This repetition (iteration) produces a sequence of complex numbers that can be described alone by their arguments. Any choice of starting angle that satisfies (1) above will produce an extremely complicated sequence of angles, that belies the simplicity of the steps. It can be shown that the sequence will be chaotic, i.e. it is sensitive to the detailed choice of starting angle. (en)
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  • 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: 1. * Choose any complex number on the unit circle whose argument (angle) is not a rational multiple of π, 2. * Repeatedly square that number. (en)
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  • Complex squaring map (en)
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