This tag is for questions relating to complex dynamics, study of dynamical systems defined by iteration of functions on complex number spaces. It was an area of research established by Fatou and Julia towards the beginning of the last century.
Complex dynamics concerns the iteration of analytic functions of one complex variable. Such iteration arises, for example, when solving complex equations by Newton’s method. For each function, the complex plane is divided into two fundamentally different parts – the Fatou set, where the behavior of the iterates is stable under local variation, and the Julia set, where it is chaotic. The subject of complex dynamics experienced a huge resurgence of interest in the 1980s, with the advent of computer graphics illustrating the highly intricate nature of most Julia sets, and the introduction of powerful new techniques from complex analysis leading to much profound new work.
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