On the Equicontinuity Region of Discrete Subgroups of PU(1,n)
| dc.creator | Seade, José | |
| dc.creator | Cano, Angel | |
| dc.date | 2008-09-09 | |
| dc.date.accessioned | 2026-07-07T10:01:44Z | |
| dc.date.available | 2026-07-07T10:01:44Z | |
| dc.description | Let $ G $ be a discrete subgroup of PU(1,n). Then $ G $ acts on $\mathbb {P}^n_\mathbb C$ preserving the unit ball $\mathbb {H}^n_\mathbb {C}$, where it acts by isometries with respect to the Bergman metric. In this work we determine the equicontinuty region $Eq(G)$ of $G$ in $\mathbb P^n_{\mathbb C}$: It is the complement of the union of all complex projective hyperplanes in $\mathbb {P}^n_{\mathbb C}$ which are tangent to $\partial \mathbb {H}^n_\mathbb {C}$ at points in the Chen-Greenberg limit set $Λ_{CG}(G )$, a closed $G$-invariant subset of $\partial \mathbb {H}^n_\mathbb {C}$, which is minimal for non-elementary groups. We also prove that the action on $Eq(G)$ is discontinuous. | |
| dc.identifier | https://arxiv.org/abs/0809.1546 | |
| dc.identifier | http://arxiv.org/abs/0809.1546 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/168728 | |
| dc.subject | Dynamical Systems | |
| dc.subject | Complex Variables | |
| dc.subject | 32Q45, 37F45 (Primary); 22E40, 57R30 (Secondary) | |
| dc.title | On the Equicontinuity Region of Discrete Subgroups of PU(1,n) | |
| dc.type | text |