Let be a metric space, and let be a homeomorphism. The -limit set of , denoted by , is the set of cluster points of the forward orbit . Hence, if and only if there is a strictly increasing sequence of natural numbers such that as .
Another way to express this is
The -limit set is defined in a similar fashion, but for the backward orbit; i.e. .
If is a continuous flow, the definition is similar: consists of those elements of for which there exists a strictly increasing sequnece of real numbers such that and as . Similarly, is the -limit set of the reversed flow (i.e. ). Again, these sets are invariant and if is compact they are compact and nonempty. Furthermore,
|Date of creation||2013-03-22 13:39:37|
|Last modified on||2013-03-22 13:39:37|
|Last modified by||Koro (127)|