双Lipschitz等价的两均匀Cantor集相似压缩不动点坐标的关系

The Relationship of Coordinate Formulas of the Contractingsimilarity Fixed Points for Two Uniforms Cantor Sets to Be Bi-Lipschitz Equivalent

首先利用双Lipschitz等价的条件,构造了满足双Lipschitz等价的两均匀Cantor集E1和E2,并研究了它们相似压缩不动点的坐标公式,同时通过一个函数建立了两坐标公式的关系。最后,对与E2满足双Lipschitz等价条件的均匀Cantor集E的相似压缩不动点坐标公式给出了一个重要猜测。

First,we construct two uniform Cantor sets E1 and E2,which to be bi-Lipschitz equivalent,using the condition of bi-Lipschitz equivalent.Then we research the coordinate formulas for the contracting-similarity fixed points of them.Moreover,we establish the relationship between two coordinate formulas using a function.At last,an important conjecture is given for the formula of the contracting-similarity fixed point of the uniform Cantor set E,and E2 are to be bi-Lipschitz equivalent.