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Article Dans Une Revue Journal of the Mathematical Society of Japan Année : 2013

Equivalence relations for two variable real analytic function germs

Résumé

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.

Dates et versions

hal-00941037 , version 1 (03-02-2014)

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Citer

Satoshi Koike, Adam Parusinski. Equivalence relations for two variable real analytic function germs. Journal of the Mathematical Society of Japan, 2013, 65 (1), pp.237-276. ⟨10.2969/jmsj/06510237⟩. ⟨hal-00941037⟩
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