# Bilipschitz equivalence of polynomials

## TL;DR

This paper investigates the bilipschitz equivalence classes of a family of two-variable polynomials, showing that while the polynomials themselves are not bilipschitz equivalent, their level curves are.

## Contribution

It introduces a family of polynomials with distinct bilipschitz classes and analyzes the relationship between their polynomials and level curves.

## Key findings

- Distinct polynomials are not bilipschitz equivalent
- Level curves of different polynomials are bilipschitz equivalent
- Provides insights into the geometric structure of polynomial level sets

## Abstract

We study a family of polynomials in two variables having moduli up to bilipschitz equivalence: two distinct polynomials of this family are not bilipschitz equivalent. However any level curve of the first polynomial is bilipschitz equivalent to a level curve of the second.