On \(\omega\)-limit sets of triangular maps (Q1803965)

The paper studies possible \(\omega\)-limit sets for triangular maps \(F: I^ 2\to I^ 2\), where \(I\) is a real compact interval. A map is called triangular if \(F(x,y)= (f(x),g(x,y))\). The main result obtained is the characterization of those \(\omega\)-limit sets which lie in one fibre (\(x=\text{const.}\)). Further, it is shown that as the intersection of an \(\omega\)-limit set with a fibre one can obtain an arbitrary compact subset of the fibre.