Science in China Series A: Mathematics

, Volume 44, Issue 3, pp 292–298 | Cite as

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

  • Xinghua Wang
  • Danfu Han


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 iteration extraneous fixed point numerical extraneous roots Sullivan’s basin fractal pictures 


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Copyright information

© Science in China Press 2001

Authors and Affiliations

  • Xinghua Wang
    • 1
    • 2
  • Danfu Han
    • 1
  1. 1.Mathematics DepartmentZhejiang UniversityHangzhouChina
  2. 2.Academy of Mathematics and System SciencesChinese Academy of SciencesBeijingChina

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