Identifying variable points on a smooth curve.
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Intersection theory on Deligne-Mumford compactifications
Eduard Looijenga (1992/1993)
Séminaire Bourbaki
Invariants of bi-Lipschitz equivalence of real analytic functions
Jean-Pierre Henry, Adam Parusiński (2004)
Banach Center Publications
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 admits 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 f(x)| is comparable to the size of |f(x)|.
Invariants polaires de courbes planes.
M. Merle (1977)
Inventiones mathematicae
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