## Equivalence relations for real analytic function germs

Satoshi Koike

Hyogo University, Japan

Abstract

Related to a coordinate change, \(C^r\) equivalences, \(1 \le r \le \omega\), are natural equivalence relations for real analytic function germs. Lipschitz equivalence is natural also in Lipschitz Geometry. On the other hand, Tzee-Char Kuo has introduced the notion of blow-analytic equivalence towards the classification of real singularities from the viewpoint of their analytic structure. In this talk we discuss the relationship between blow-analytic equivalence and \(C^r\) equivalence or Lipschitz equivalence.