This article is cited in 1 paper

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

Lyudmila S. Efremova^ab, Dmitry A. Novozhilov<sup>b

a</sup> Moscow Institute of Physics and Technology, Institutsky per. 9, 141701 Dolgoprudny, Russia
^b Nizhny Novgorod State University, pr. Gagarina 23, 603022 Nizhny Novgorod, Russia

Abstract: 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.

Keywords: skew product of interval maps, quotient map, fiber maps, chain-recurrent point, weakly non-wandering point, $\Omega$-blowup, topological entropy

MSC: 37C05, 37Exx, 37Gxx, 37C50, 37C25, 37B40

Received: 14.10.2024
Accepted: 28.12.2024

Language: English

DOI: 10.1134/S156035472501006X