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Equivalence Relations for Two Variable Real Analytic Function Germs by Koike, Satoshi; Parusinski, Adam is a scholarly article available to read on EtoBox.

What is Equivalence Relations for Two Variable Real Analytic Function Germs about?

For two variable real analytic function germs we compare the blow-analytic equivalence in the sense of Kuo to the other natural equivalence relations. Our main theorem states that $C^1$ equivalent germs are blow-analytically equivalent. This gives a negative answer to a conjecture of Kuo. In the proof we show that the Puiseux pairs of real Newton-Puiseux roots are preserved by the $C^1$ equivalence of function germs. The proof is achieved, being based on a combinatorial characterisation of blow-analytic equivalence in terms of the real tree model. We also give several examples of bi-Lipschitz equivalent germs that are not blow-analytically equivalent.

Author

Koike, Satoshi; Parusinski, Adam

Published

2008

Language

EN