Equivalence relations for two variable real analytic function germs

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概要

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• For two variable real analytic function germs we compare the blow-analytic equivalence in the sense of Kuo to other natural equivalence relations. Our main theorem states that C1 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 C1 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.

著者

• Koike Satoshi

  Department Of Mathematics Hyogo University Of Teacher Education

• Parusiński Adam

  Laboratoire J. A. Dieudonné U.M.R. C.N.R.S. N 6621, Université de Nice Sophia-Antipolis

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