On the asymptotic behavior of the trajectories of skew products with a closed set of periodic points
https://doi.org/10.26907/2949-3919.2025.3.58-86
Abstract
The article continues the research of the asymptotic behavior of the trajectories of the most simple skew products on multidimensional cells conducted by the authors. Here we describe the structure of nonwandering set of continuous skew products having a closed set of periodic points and such that the set of (least) periods of periodic points is unbounded. An example of a differentiable skew product with a closed set of periodic points is constructed, defined on an n-dimensional cell (n ≥ 3) and having a one-dimensional ω-limit set. Keywords: skew product, nonwandering set, Ω-blow up, ω-limit set
Supporting agencies: The work is supported by the Russian Science Foundation (grant no. 24-21-00242)
About the Authors
L. S. Efremova
Lobachevskii Nizgny Novgorod State University; Moscow Institute of Physics and Technology
Russian Federation
Russian Federation
Lyudmila Sergeevna Efremova
23 Gagarin ave., Nizhny Novgorod 603022;
9 Institutskii alley, Dolgoprudny, Moscow Region, 141701
M. V. Shalagin
Lobachevskii Nizgny Novgorod State University
Russian Federation
Russian Federation
Matvey Andreevich Shalagin
23 Gagarin ave., Nizhny Novgorod 603022
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Review
For citations:
Efremova L.S., Shalagin M.V. On the asymptotic behavior of the trajectories of skew products with a closed set of periodic points. Mathematics and Theoretical Computer Science. 2025;3(3):58-86. (In Russ.) https://doi.org/10.26907/2949-3919.2025.3.58-86
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