On the bi-Lipschitz contact equivalence of plane complex function-germs
نویسندگان
چکیده
منابع مشابه
A Criterion for the Topological Equivalence of Two Variable Complex Analytic Function Germs
We show that two analytic function germs (C, 0) → (C, 0) are topologically right equivalent if and only if there is a one-to-one correspondence between the irreducible components of their zero sets, that preserves the multiplicites of these components, their Puiseux pairs, and the intersection numbers of any pairs of distinct components. By Zariski [7] and Burau [1], the topological type of an ...
متن کاملInvariants of Bi-lipschitz Equivalence of Real Analytic Functions
We construct an invariant of the bi-Lipschitz equivalence of analytic function germs (Rn,0) → (R,0) that varies continuously in many analytic families. This shows that the bi-Lipschitz equivalence of analytic function germs admit continuous moduli. For a germ f the invariant is given in terms of the leading coefficients of the asymptotic expansions of f along the sets where the size of |x||grad...
متن کاملA Criterion for Topological Equivalence of Two Variable Complex Analytic Function Germs
We show that two analytic function germs (C, 0) → (C, 0) are topologically right equivalent if and only if there is a one-to-one correspondence between the irreducible components of their zero sets that preserves the multiplicites of these components, their Puiseux pairs, and the intersection numbers of any pairs of distinct components. By Zariski [10] and Burau [2], the topological type of an ...
متن کاملBlow-analytic Equivalence of Two Variable Real Analytic Function Germs
Blow-analytic equivalence is a notion for real analytic function germs, introduced by Tzee-Char Kuo in order to develop the real analytic equisingularity theory. In this paper we give several complete characterisations of blow-analytic equivalence in the two dimensional case in terms of the minimal resolutions, the real tree model for the arrangement of Newton-Puiseux roots, and the cascade blo...
متن کاملEquivalence Relations for Two Variable Real Analytic Function Germs
For two variable real analytic function germs we compare the blowanalytic equivalence in the sense of Kuo to the other natural equivalence relations. Our main theorem states that C 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 equivalence of f...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Singularities
سال: 2015
ISSN: 1949-2006
DOI: 10.5427/jsing.2015.13a