Asymptotic Behavior of Individual Orbits of Discrete Systems
| dc.creator | Van Minh, Nguyen | |
| dc.date | 2008-11-04 | |
| dc.date | 2008-12-28 | |
| dc.date.accessioned | 2026-07-07T12:22:10Z | |
| dc.date.available | 2026-07-07T12:22:10Z | |
| dc.description | We consider the asymptotic behavior of bounded solutions of the difference equations of the form $x(n+1)=Bx(n) + y(n)$ in a Banach space $\X$, where $n=1,2,...$, $B$ is a linear continuous operator in $\X$, and $(y(n))$ is a sequence in $\X$ converging to 0 as $n\to\infty$. An obtained result with an elementary proof says that if $σ(B) \cap \{|z|=1\} \subset \{1\}$, then every bounded solution $x(n)$ has the property that $\lim_{n\to\infty} (x(n+1)-x(n)) =0$. This result extends a theorem due to Katznelson-Tzafriri. Moreover, the techniques of the proof are furthered to study the individual stability of solutions of the discrete system. A discussion on further extensions is also given. | |
| dc.identifier | https://arxiv.org/abs/0811.0544 | |
| dc.identifier | http://arxiv.org/abs/0811.0544 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/213562 | |
| dc.subject | Dynamical Systems | |
| dc.subject | Functional Analysis | |
| dc.subject | 47D06 | |
| dc.title | Asymptotic Behavior of Individual Orbits of Discrete Systems | |
| dc.type | text |