Distribution of rational maps with a preperiodic critical point
| dc.creator | Dujardin, Romain | |
| dc.creator | Favre, Charles | |
| dc.date | 2006-01-25 | |
| dc.date | 2007-08-30 | |
| dc.date.accessioned | 2026-07-07T08:26:32Z | |
| dc.date.available | 2026-07-07T08:26:32Z | |
| dc.description | Let {f_t} be any algebraic family of rational maps of a fixed degree, with a marked critical point c(t). We first prove that the hypersurfaces of parameters for which c(t) is periodic converge as a sequence of positive closed (1,1) currents to the bifurcation current attached to c and defined by DeMarco. We then turn our attention to the parameter space of polynomials of a fixed degree d. By intersecting the d-1 currents attached to each critical point of a polynomial, Bassaneli and Berteloot obtained a positive measure of finite mass which is supported on the connectedness locus. They showed that its support is included in the closure of the set of parameters admitting d-1 neutral cycles. We show that the support of this measure is precisely the closure of the set of strictly critically finite polynomials (i.e. of Misiurewicz points). | |
| dc.description | 45 pages. Final version. To appear in American Math. Journal | |
| dc.identifier | https://arxiv.org/abs/math/0601612 | |
| dc.identifier | http://arxiv.org/abs/math/0601612 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/136969 | |
| dc.subject | Dynamical Systems | |
| dc.subject | Complex Variables | |
| dc.subject | 37F45; 32H50 | |
| dc.title | Distribution of rational maps with a preperiodic critical point | |
| dc.type | text |