Science in China Series A: Mathematics

, Volume 44, Issue 3, pp 292–298

Extraneous fixed points of Euler iteration and corresponding Sullivan’s basin


  • Xinghua Wang
    • Mathematics DepartmentZhejiang University
    • Academy of Mathematics and System SciencesChinese Academy of Sciences
  • Danfu Han
    • Mathematics DepartmentZhejiang University

DOI: 10.1007/BF02878709

Cite this article as:
Wang, X. & Han, D. Sci. China Ser. A-Math. (2001) 44: 292. doi:10.1007/BF02878709


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.


Euler iterationextraneous fixed pointnumerical extraneous rootsSullivan’s basinfractal pictures

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© Science in China Press 2001