# Lipschitz equivalence of Cantor sets and irreducibility of polynomials

## TL;DR

This paper develops a method to determine Lipschitz equivalence of certain Cantor sets using polynomial irreducibility, showing equivalence depends on contraction vectors when one is homogeneous.

## Contribution

It introduces an effective approach linking polynomial irreducibility to Lipschitz equivalence of Cantor sets, especially for two- and three-branch cases.

## Key findings

- Lipschitz equivalence can be characterized via polynomial irreducibility.
- Two Cantor sets are Lipschitz equivalent if contraction vectors are equivalent with a homogeneous vector.
- The method applies to Cantor sets with two or three branches.

## Abstract

In the paper, we provide an effective method for the Lipschitz equivalence of two-branch Cantor sets and three-branch Cantor sets by studying the irreducibility of polynomials. We also find that any two Cantor sets are Lipschitz equivalent if and only if their contraction vectors are equivalent provided one of the contraction vectors is homogeneous.