Pinching of polynomials.
Summary: Let \(f_0: \mathbb{C} \to \mathbb{C}\) be a semi-hyperbolic polynomial in the sense of Carleson-Jones-Yoccoz with an attracting point. The goal of this paper is to show that one can define a semi-hyperbolic deformation \((f_t)_{t\geq 0}\) such that the attracting cycle becomes parabolic for the limit polynomial \(f_\infty\) and that \(f_0\) and \(f_\infty\) are semi-conjugate. This deformation is defined by pinching curves in appropriate quotient spaces.
scientific article; zbMATH DE number 1756812