On Closed Invariant Sets in Local Dynamics
| dc.creator | Bisi, Cinzia | |
| dc.date | 2007-01-23 | |
| dc.date | 2008-08-13 | |
| dc.date.accessioned | 2026-07-07T09:56:16Z | |
| dc.date.available | 2026-07-07T09:56:16Z | |
| dc.description | We investigate the dynamical behaviour of a holomorphic map on a $f-$invariant subset $\mathcal{C}$ of $U,$ where $f:U \to \mathbb{C}^k.$ We study two cases: when $U$ is an open, connected and polynomially convex subset of $\mathbb{C}^k$ and $\mathcal{C} \subset \subset U,$ closed in $U,$ and when $\partial U$ has a p.s.h. barrier at each of its points and $\mathcal{C}$ is not relatively compact in $U.$ In the second part of the paper, we prove a Birkhoff's type Theorem for holomorphic maps in several complex variables, i.e. given an injective holomorphic map $f,$ defined in a neighborhood of $\overline{U},$ with $U$ star-shaped and $f(U)$ a Runge domain, we prove the existence of a unique, forward invariant, maximal, compact and connected subset of $\overline{U}$ which touches $\partial U.$ | |
| dc.description | Exposition has been improved; Corollary 3.6 has been corrected; 8 pages; version close to be published | |
| dc.identifier | https://arxiv.org/abs/math/0701639 | |
| dc.identifier | http://arxiv.org/abs/math/0701639 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/166923 | |
| dc.subject | Complex Variables | |
| dc.subject | Dynamical Systems | |
| dc.subject | 32A07,32A99,32H50,58F12 (Primary) 37F10,58F23,30D05 (Secondary) | |
| dc.title | On Closed Invariant Sets in Local Dynamics | |
| dc.type | text |