Hyperbolic components of polynomials with a fixed critical point of maximal order
| dc.creator | Roesch, Pascale | |
| dc.date | 2006-12-06 | |
| dc.date.accessioned | 2026-07-07T07:34:43Z | |
| dc.date.available | 2026-07-07T07:34:43Z | |
| dc.description | For the study of the 2-dimensional space of cubic polynomials, J. Milnor considers the complex 1-dimensional slice S_n of the cubic polynomials which have a super-attracting orbit of period n. He gives in [M4] a detailed conjectural picture of S_n. In this article, we prove these conjectures for S_1 and generalize these results in higher degrees. In particular, this gives a description of the closures of the hyperbolic components and of the Mandelbrot copies sitting in the connectedness locus. We prove that the closure of hyperbolic components is a Jordan curve, the points of which are characterized according to their dynamical behaviour. The global picture of the connectedness locus is a closed disk together with ``limbs'' sprouting off at the cusps of Mandelbrot copies and whose diameter tends to 0 (which corresponds to the Yoccoz inequality in the quadratic case). [[M4] J. Milnor - On cubic polynomials with periodic critical point, preprint (1991).] | |
| dc.identifier | https://arxiv.org/abs/math/0612172 | |
| dc.identifier | http://arxiv.org/abs/math/0612172 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/119863 | |
| dc.subject | Dynamical Systems | |
| dc.subject | 37F10 | |
| dc.title | Hyperbolic components of polynomials with a fixed critical point of maximal order | |
| dc.type | text |