Commuting semigroups of holomorphic mappings
| dc.creator | Elin, Mark | |
| dc.creator | Levenshtein, Marina | |
| dc.creator | Reich, Simeon | |
| dc.creator | Shoikhet, David | |
| dc.date | 2006-09-30 | |
| dc.date.accessioned | 2026-07-07T07:28:33Z | |
| dc.date.available | 2026-07-07T07:28:33Z | |
| dc.description | Let $S_{1}=\left\{F_t\right\}_{t\geq 0}$ and $S_{2}=\left\{G_t\right\}_{t\geq 0}$ be two continuous semigroups of holomorphic self-mappings of the unit disk $Δ=\{z:|z|<1\}$ generated by $f$ and $g$, respectively. We present conditions on the behavior of $f$ (or $g$) in a neighborhood of a fixed point of $S_{1}$ (or $S_{2}$), under which the commutativity of two elements, say, $F_1$ and $G_1$ of the semigroups implies that the semigroups commute, i.e., $F_{t}\circ G_{s}=G_{s}\circ F_{t}$ for all $s,t\geq 0$. As an auxiliary result, we show that the existence of the (angular or unrestricted) $n$-th derivative of the generator $f$ of a semigroup $\left\{F_t\right\}_{t\geq 0}$ at a boundary null point of $f$ implies that the corresponding derivatives of $F_{t}$, $t\geq 0$, also exist, and we obtain formulae connecting them for $n=2,3$. | |
| dc.identifier | https://arxiv.org/abs/math/0610027 | |
| dc.identifier | http://arxiv.org/abs/math/0610027 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/117770 | |
| dc.subject | Complex Variables | |
| dc.subject | Dynamical Systems | |
| dc.title | Commuting semigroups of holomorphic mappings | |
| dc.type | text |