Lyudmila Efremova
Publications:
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Efremova L. S., Novozhilov D. A.
Chain-Recurrent $C^0$- $\Omega$-Blowup in $C^1$-Smooth Simplest Skew Products on Multidimensional Cells
2025, vol. 30, no. 1, pp. 120-140
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.
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Efremova L. S.
$C^1$-Smooth $\Omega$-Stable Skew Products and Completely Geometrically Integrable Self-Maps of 3D-Tori, I: $\Omega$-Stability
2024, vol. 29, no. 3, pp. 491-514
Abstract
We prove here the criterion of $C^1$- $\Omega$-stability of self-maps of a 3D-torus, which
are skew products of circle maps. The $C^1$- $\Omega$-stability property is studied with respect to homeomorphisms of skew products type. We give here an example of the $\Omega$-stable map on a 3D-torus and investigate approximating properties of maps under consideration.
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