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A bi-Lipschitz invariant for analytic function germs

Nhan Nguyen

Abstract

In this paper, we introduce a new bi-Lipschitz invariant for analytic function germs in two variables, enhancing the Henry-Parusinski invariant.

A bi-Lipschitz invariant for analytic function germs

Abstract

In this paper, we introduce a new bi-Lipschitz invariant for analytic function germs in two variables, enhancing the Henry-Parusinski invariant.

Paper Structure

This paper contains 5 sections, 3 theorems, 72 equations.

Table of Contents

  1. Introduction
  2. Main result
  3. Păunescu--Tibăr's results
  4. New invariant
  5. Examples

Key Result

Theorem 2.2

Let $f, g: (\mathbb{C}^2, 0) \rightarrow (\mathbb{C}, 0)$ be analytic function germs that are mini-regular in $x$ and have no multiple roots. Suppose that there exists a bi-Lipschitz homeomorphic germ $\varphi: (\mathbb{C}^2, 0) \rightarrow (\mathbb{C}^2, 0)$ such that $f = g \circ \varphi$. Let $\a

Theorems & Definitions (10)

  • Example 2.1
  • Theorem 2.2: PT
  • Remark 2.3
  • Lemma 2.4
  • proof
  • Theorem 2.5
  • Example 3.1
  • proof
  • Example 3.2
  • proof