Аннотация:
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.
Ключевые слова:
skew product of interval maps, quotient map, fiber maps, chain-recurrent point, weakly non-wandering point, $\Omega$-blowup, topological entropy
Список литературы