Nonwandering set of points of skew-product maps with base having closed set of periodic points

The aim of the present paper is to study the structure of the nonwandering set of points Ω(⋅) for the skew-product maps of the unit square I2=[0,1]×[0,1], (x,y)→(f(x),g(x,y)), with base f having closed set of periodic points. For every and every point (x,y) with x periodic of period px by f and y not chain recurrent of Fpx|Ix, where Ix={x}×I, we prove that (x,y)∉Ω(F). On the other hand we construct a map with an isolated fixed point x0 of f and y0∉Ω(F|Ix0) such that (x0,y0)∈Ω(F0).