The boundary of the moduli space of quadratic rational maps
| dc.creator | DeMarco, Laura | |
| dc.date | 2004-12-21 | |
| dc.date.accessioned | 2026-07-07T05:15:34Z | |
| dc.date.available | 2026-07-07T05:15:34Z | |
| dc.description | Let $M_2$ be the space of quadratic rational maps $f:{\bf P}^1\to{\bf P}^1$, modulo the action by conjugation of the group of Möbius transformations. In this paper a compactification $X$ of $M_2$ is defined, as a modification of Milnor's $\bar{M}_2\iso{\bf CP}^2$, by choosing representatives of a conjugacy class $[f]\in M_2$ such that the measure of maximal entropy of $f$ has conformal barycenter at the origin in ${\bf R}^3$, and taking the closure in the space of probability measures. It is shown that $X$ is the smallest compactification of $M_2$ such that all iterate maps $[f]\mapsto [f^n]\in M_{2^n}$ extend continuously to $X \to \bar{M}_{2^n}$, where $\bar{M}_d$ is the natural compactification of $M_d$ coming from geometric invariant theory. | |
| dc.description | 38 pages, 3 figures | |
| dc.identifier | https://arxiv.org/abs/math/0412438 | |
| dc.identifier | http://arxiv.org/abs/math/0412438 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/73669 | |
| dc.subject | Dynamical Systems | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 37F45 | |
| dc.title | The boundary of the moduli space of quadratic rational maps | |
| dc.type | text |