Iteration at the boundary of the space of rational maps
| dc.creator | DeMarco, Laura | |
| dc.date | 2004-03-03 | |
| dc.date | 2004-12-21 | |
| dc.date.accessioned | 2026-07-07T05:05:55Z | |
| dc.date.available | 2026-07-07T05:05:55Z | |
| dc.description | Let $Rat_d$ denote the space of holomorphic self-maps of ${\bf P}^1$ of degree $d\geq 2$, and $μ_f$ the measure of maximal entropy for $f\in Rat_d$. The map of measures $f\mapstoμ_f$ is known to be continuous on $Rat_d$, and it is shown here to extend continuously to the boundary of $Rat_d$ in $\bar{Rat}_d \simeq {\bf P}^{2d+1}$, except along a locus $I(d)$ of codimension $d+1$. The set $I(d)$ is also the indeterminacy locus of the iterate map $f\mapsto f^n$ for every $n\geq 2$. The limiting measures are given explicitly, away from $I(d)$. The degenerations of rational maps are also described in terms of metrics of non-negative curvature on the Riemann sphere: the limits are polyhedral. | |
| dc.description | 25 pages | |
| dc.identifier | https://arxiv.org/abs/math/0403078 | |
| dc.identifier | http://arxiv.org/abs/math/0403078 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70350 | |
| dc.subject | Dynamical Systems | |
| dc.subject | Complex Variables | |
| dc.title | Iteration at the boundary of the space of rational maps | |
| dc.type | text |