Abstract
The phenomenon of “numerical extraneous roots” of Euler’s iteration has been found. By systematic searching, some polynomials and the corresponding initial values are given, which make the fixed points of Euler’s iteration not the roots of the polynomials. For those repelling extraneous fixed points, the adjoint dynamical types of Sullivan’s basins are also studied. Finally, the fractal pictures are produced.
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Wang, X., Han, D. Extraneous fixed points of Euler iteration and corresponding Sullivan’s basin. Sci. China Ser. A-Math. 44, 292–298 (2001). https://doi.org/10.1007/BF02878709
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DOI: https://doi.org/10.1007/BF02878709