The phenomenon of “numerical extraneous roots” of Euler'siteration has been found. By systematic searching, some polynomials and the corresponding initial values are given, which make the fixed points of Euler&#...The phenomenon of “numerical extraneous roots” of Euler'siteration 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.展开更多
基金This work was supported by the Special Funds for Major State Basic Research Projects ( Grant No. 19990328) the Natural Science Foundation of Zhejiang Province (Grant No. 100002) .
文摘The phenomenon of “numerical extraneous roots” of Euler'siteration 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.
