Chain-Recurrent $$C^{0}$$- $$\Omega$$-Blowup in $$C^{1}$$-Smooth Simplest Skew Products on Multidimensional Cells

In this paper we prove criteria of a $$C^{0}$$ - $$\Omega$$ -blowup in $$C^{1}$$ -smooth skew products with a closed set of periodic points on multidimensional cells and give examples of maps that admit such a $$\Omega$$ -blowup. Our method is based on the study of the properties of the set of chain-recurrent points. We also prove that the set of weakly nonwandering points of maps under consideration coincides with the chain-recurrent set, investigate the approximation (in the $$C^{0}$$ -norm) and entropy properties of $$C^{1}$$ -smooth skew products with a closed set of periodic points.