Newton's Method, Circle Maps, and Chaotic Motion
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Publication:3314614
DOI10.2307/2322163zbMath0532.58016OpenAlexW4238660120WikidataQ55981619 ScholiaQ55981619MaRDI QIDQ3314614
John B. Urenko, Donald G. Saari
Publication date: 1984
Published in: The American Mathematical Monthly (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.2307/2322163
Related Items (23)
Multiple attractors in Newton's method ⋮ How to be sure of finding a root of a complex polynomial using Newton's method ⋮ Extraneous fixed points, basin boundaries and chaotic dynamics for Schröder and König rational iteration functions ⋮ Improbability of nonconvergent chaos in Newton's method ⋮ On the efficiency of algorithms of analysis ⋮ Some informational requirements for convergence ⋮ FINITENESS OF THE AREA OF BASINS OF ATTRACTION OF RELAXED NEWTON METHOD FOR CERTAIN HOLOMORPHIC FUNCTIONS ⋮ Improbability of nonconvergence in a cubic root-finding method ⋮ Newton's method and complex dynamical systems ⋮ Newton's method for fractal approximation ⋮ CONJECTURES ABOUT SIMPLE DYNAMICS FOR SOME REAL NEWTON MAPS ON ℝ2 ⋮ On the dynamics of a third order Newton's approximation method ⋮ Dynamics of Newton Maps of Quadratic Polynomial Maps of ℝ2 into Itself ⋮ On the existence of universally convergent mechanisms ⋮ The ultimate of chaos resulting from weighted voting systems ⋮ Chaotic dynamics of a third-order Newton-type method ⋮ Rotation intervals for a class of maps of the real line into itself ⋮ Rational functions and pseudo-Newton algorithms ⋮ An example for the Regula-falsi method with an asymptotic cycle ⋮ Exhibiting chaos and fractals with a microcomputer ⋮ Chaotic Numerics From an Integrable Hamiltonian System ⋮ Chaotic phenomena ⋮ Symbolic dynamics of the cubic map
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