Let 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 such that the attracting cycle becomes parabolic for the limit polynomial and that and are semi-conjugate. This deformation is defined by pinching curves in appropriate quotient spaces.
Cite this article
Peter Haïssinsky, Pincement de polynômes. Comment. Math. Helv. 77 (2002), no. 1, pp. 1–23DOI 10.1007/S00014-002-8329-Z