Immediate and virtual basins of Newton's method for entire functions.
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Publication:2488753
DOI10.5802/aif.2184zbMath1103.30015arXivmath/0403336OpenAlexW1490101027MaRDI QIDQ2488753
Sebastian Mayer, Dierk Schleicher
Publication date: 15 May 2006
Published in: Annales de l'Institut Fourier (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0403336
Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10) Dynamical systems in numerical analysis (37N30)
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Cites Work
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- Dynamic rays of bounded-type entire functions
- On infinite area for complex exponential function
- On the number of iterations of Newton's method for complex polynomials
- On the efficiency of algorithms of analysis
- Iteration and the Solution of Functional Equations for Functions Analytic In the Unit Disk
- Newton’s method on the complex exponential function
- Iteration of meromorphic functions
- Weakly repelling fixpoints and the connectivity of wandering domains
- Virtual immediate basins of Newton maps and asymptotic values
- How to find all roots of complex polynomials by Newton's method.
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