Abstract:
We consider continuous skew products on n-dimensional (n > 1)
manifolds such as cells, cylinders, and tori, and introduce the notion of weakly nonwandering points
with respect to the family of mappings in layers over wandering points of the factor mapping.
We prove a criterion for the existence of such points in terms of the $?$-explosion (in the $C^0$-norm) in the mappings
in layers over the limit (for a wandering set) non-wandering points of the factor mapping.
Using the obtained results, we describe the structure of the nonwandering set of skew products
on $n$-dimensional cells, cylinders and tori.
