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On the $$\omega$$-limit sets of product maps. (English) Zbl 1219.37031
The authors consider the Cartesian product of a finite collection of continuous interval maps. For this dynamical system, they construct the $$\omega$$-limit set, namely the union of the limit points of each orbit. They prove that this set is equal to the Cartesian product of the $$\omega$$-limit sets of the individual components.

##### MSC:
 37E05 Dynamical systems involving maps of the interval (piecewise continuous, continuous, smooth) 54H20 Topological dynamics (MSC2010) 37E99 Low-dimensional dynamical systems 37B99 Topological dynamics
##### Keywords:
product maps; $$\omega$$-limit sets