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Fractal Newton basins. (English) Zbl 1104.37034
Summary: The dynamics of complex cubic polynomials have been studied extensively in the recent years. The main interest in this work is to focus on the Julia sets in the dynamical plane, and then is consecrated to the study of several topics in more detail. Newton’s method is considered since it is the main tool for finding solutions to equations, which leads to some fantastic images when it is applied to complex functions and gives rise to a chaotic sequence.
MSC:
37F10Polynomials; rational maps; entire and meromorphic functions
37D45Strange attractors, chaotic dynamics
37E05Maps of the interval (piecewise continuous, continuous, smooth)
37F50Small divisors, rotation domains and linearization; Fatou and Julia sets
65H05Single nonlinear equations (numerical methods)