Lipschitz Equivalence Of Self-similar Sets And Irreducibility Of Polynomials

In the thesis,we make a general description on the recent researches in the Lipschitz equivalence of Self-similar sets.And provide an effective method for the Lipschitz equivalence of two-branch Cantor sets and three-branch Cantor sets by studying the irreducibility of quadrinomials.We also rediscover that two Cantor sets are Lipschitz equivalence if and only if their contraction vectors are equivalent provided one of the contraction vectors is homogeneous.