Deformations of Functions Without Real Critical Points

Abstract

Given a real analytic function f(x, y) with one critical point P ₀, we study deformations f _t of fsuch that, for any t ≠ 0, the analytic function f _t has no critical points in a neighborhood of P ₀. We give explicitly a deformation without real critical points for any function which has only one real branch with characteristic exponents (4, 2q, r).

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