The random case of Conley's theorem
| dc.creator | Liu, Zhenxin | |
| dc.date | 2005-03-26 | |
| dc.date | 2005-12-09 | |
| dc.date.accessioned | 2026-07-07T06:39:40Z | |
| dc.date.available | 2026-07-07T06:39:40Z | |
| dc.description | The well-known Conley's theorem states that the complement of chain recurrent set equals the union of all connecting orbits of the flow $ϕ$ on the compact metric space $X$, i.e. $X-\mathcal{CR}(ϕ)=\bigcup [B(A)-A]$, where $\mathcal{CR}(ϕ)$ denotes the chain recurrent set of $ϕ$, $A$ stands for an attractor and $B(A)$ is the basin determined by $A$. In this paper we show that by appropriately selecting the definition of random attractor, in fact we define a random local attractor to be the $ω$-limit set of some random pre-attractor surrounding it, and by considering appropriate measurability, in fact we also consider the universal $σ$-algebra $\mathcal F^u$-measurability besides $\mathcal F$-measurability, we are able to obtain the random case of Conley's theorem. | |
| dc.description | 15 pages | |
| dc.identifier | https://arxiv.org/abs/math/0503617 | |
| dc.identifier | http://arxiv.org/abs/math/0503617 | |
| dc.identifier | Nonlinearity 19 (2006), 277-291. http://www.iop.org | |
| dc.identifier | doi:10.1088/0951-7715/19/2/002 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/101159 | |
| dc.subject | Dynamical Systems | |
| dc.subject | 37H99; 11B37; 37B35; 37B20; 37B25 | |
| dc.title | The random case of Conley's theorem | |
| dc.type | text |