On the \(\omega\)-limit sets of product maps. (English) Zbl 1219.37031

Jiménez López, V.; Kupka, J.; Linero, A.

Dyn. Syst. Appl. 19, No. 3-4, 667-678 (2010).

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.

Reviewer: Franco Vivaldi (London)

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