Iterated Monodromy Groups
| dc.creator | Nekrashevych, Volodymyr | |
| dc.date | 2003-12-16 | |
| dc.date.accessioned | 2026-07-07T05:03:57Z | |
| dc.date.available | 2026-07-07T05:03:57Z | |
| dc.description | We associate a group $IMG(f)$ to every covering $f$ of a topological space $M$ by its open subset. It is the quotient of the fundamental group $π_1(M)$ by the intersection of the kernels of its monodromy action for the iterates $f^n$. Every iterated monodromy group comes together with a naturally defined action on a rooted tree. We present an effective method to compute this action and show how the dynamics of $f$ is related to the group. In particular, the Julia set of $f$ can be reconstructed from $\img(f)$ (from its action on the tree), if $f$ is expanding. | |
| dc.description | about 40 pages, 6 figures | |
| dc.identifier | https://arxiv.org/abs/math/0312306 | |
| dc.identifier | http://arxiv.org/abs/math/0312306 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69617 | |
| dc.subject | Dynamical Systems | |
| dc.subject | Group Theory | |
| dc.subject | 20E08; 37B10; 28A80 | |
| dc.title | Iterated Monodromy Groups | |
| dc.type | text |