满足递推式紧集的Lipschitz等价性

Lipschitz Equivalence of Compact Sets with a Recurrence Equation

设紧集U满足一个不交并递推式,U=(rU+(?))∪U_1.证明了若U_1与一个满足强分离条件的自相似集T Lipschitz等价,则U与T也是Lipschitz等价.并举例说明定理在自相似并集间的Lipschitz等价中的应用.

Let U be a compact set satisfying a recurrence equation U -- （rU ＋ O） U u1, which is a disjoint union. The author proves that U is Lipschitz equivalent to a self-similar set T with the strong separated condition if U1 is Lipschitz equivalent to T. Some examples are provided to illuminate the application of the theory in the Lipschitz equivalence among the unions of self-similar sets.