Multiple attractors in Newton's method

DOI10.1017/S0143385700003692zbMath0584.58028MaRDI QIDQ3706983

Hurley, Mike

Publication date: 1986

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

zbMATH Keywords

complex planeattracting periodic orbits

Mathematics Subject Classification ID

Attractors and repellers of smooth dynamical systems and their topological structure (37C70) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45)

Related Items (9)

How to be sure of finding a root of a complex polynomial using Newton's method ⋮ Newton's method and complex dynamical systems ⋮ Superattracting cycles of the relaxed Newton's method for entire functions ⋮ Prescribed cycles of König's method for polynomials ⋮ Some Connections of Complex Dynamics ⋮ On infinite area for complex exponential function ⋮ Negativity of Lyapunov exponents and convergence of generic random polynomial dynamical systems and random relaxed Newton's methods ⋮ Rayleigh Quotient Iteration for Nonsymmetric Matrices ⋮ Newton’s method on the complex exponential function

Cites Work

• Unnamed Item
• On the iteration of a rational function: Computer experiments with Newton's method
• Newton's Method and Symbolic Dynamics
• Complex analytic dynamics on the Riemann sphere
• Newton's Method, Circle Maps, and Chaotic Motion
• Newton’s Algorithm and Chaotic Dynamical Systems
• The fundamental theorem of algebra and complexity theory

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