Cayley's problem

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Cayley's problem. (English). Aplikace matematiky, vol. 35 (1990), issue 2, pp. 140-146

MSC: 39A10 | MR 1042849 | Zbl 0709.39001

Keywords:
Newton method; difference equation; series expansion, fixed point; discrete dynamical system; Julia set

References:

[1] A. Cayley: The Newton-Fourier imaginary problem. Amer. J. Math. II, 97 (1879).

[2] P. Petek: A Nonconverging Newton Sequence. Math. Magazine 56, no. 1, 43 - 45 (1983). MR 0692174 | Zbl 0505.10006

[3] G. Julia: Sur l'iteration des fonctions rationnelles. Journal de Math. Pure et Appl. 8, 47-245 (1918).

[4] P. Fatou: Sur les equations fonctionelles. Bull. Soc. Math. France, 47: 161 - 271, 48: 33 - 94, 208-314 (1919). MR 1504787

[5] H. O. Peitgen D. Saupe F. Haeseler: Cayley's Problem and Julia Sets. Math. Intelligencer 6: 11-20 (1984). MR 0738904

[6] P. Blanchard: Complex Analytic Dynamics on the Riemann Sphere. Bull. Amer. Math. Soc. 11, 85-141 (1984). MR 0741725 | Zbl 0558.58017

[7] C. L. Siegel: Iteration of Analytic Functions. Annals of Mathematics 43, 607-612 (1942). MR 0007044 | Zbl 0061.14904

[8] H. O. Peitgen P. H. Richter: The Beauty of Fractals. Springer-Verlag, Berlin, Heidelberg 1986. MR 0852695

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