Name
Abstract | ||
|---|---|---|
In this paper, we study chaos for bounded operators on Banach spaces. First, it is proved that, for a bounded operator T defined on a Banach space, Li–Yorke chaos, Li–Yorke sensitivity, spatio-temporal chaos, and distributional chaos in a sequence are equivalent, and they are all strictly stronger than sensitivity. Next, we show that T is sensitive dependence iff sup{‖Tn‖:n∈N}=∞. Finally, the following results are obtained: (1) T is chaotic iff Tn is chaotic for each n∈N. (2) The product operator Tn∗=∏i=1nTi is chaotic iff Tk is chaotic for some k∈{1,2,…,n}. |
Year | DOI | Venue |
|---|---|---|
2012 | 10.1016/j.aml.2011.09.055 | Applied Mathematics Letters |
Keywords | Field | DocType |
Li–Yorke chaos,Li–Yorke sensitivity,Spatio-temporal chaos,Distributional chaos in a sequence,Irregular vector,Bounded operator | Discrete mathematics,Bounded operator,Operator product expansion,Mathematical analysis,Banach space,Equivalence (measure theory),Operator (computer programming),Chaotic,Mathematics,Bounded function | Journal |
Volume | Issue | ISSN |
25 | 3 | 0893-9659 |
Citations | PageRank | References |
3 | 0.78 | 0 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Xinxing Wu | 1 | 68 | 18.44 |
| Peiyong Zhu | 2 | 59 | 8.68 |