Commentarii Mathematici Helvetici

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Volume 77, Issue 1, 2002, pp. 1–23
DOI: 10.1007/s00014-002-8329-z

Published online: 2002-03-31

Pincement de polynômes

Peter Haïssinsky[1]

(1) Université Paul Sabatier, Toulouse, France

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\ge 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.

Keywords: Ensemble de Julia, déformation quasiconforme, point parabolique, polynôme semi-hyperbolique

Haïssinsky Peter: Pincement de polynômes. Comment. Math. Helv. 77 (2002), 1-23. doi: 10.1007/s00014-002-8329-z