JournalscmhVol. 77 , No. 1DOI 10.1007/s00014-002-8329-z

Pincement de polynômes

  • Peter Haïssinsky

    Université Paul Sabatier, Toulouse, France
Pincement de polynômes cover

Abstract

Let f0:CCf_{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 (ft)t0(f_{t})_{t\ge 0} such that the attracting cycle becomes parabolic for the limit polynomial ff_{\infty} and that f0f_{0} and ff_{\infty} are semi-conjugate. This deformation is defined by pinching curves in appropriate quotient spaces.