Structure of sets of semicontinuous points of \(\varepsilon\)-capacity of non-autonomous dynamical systems continuously depending on a parameter. (English. Russian original) Zbl 1468.37019
Mosc. Univ. Math. Bull. 75, No. 6, 246-252 (2020); translation from Vestn. Mosk. Univ., Ser. I 75, No. 6, 19-26 (2020).
Summary: For a family of non-autonomous dynamical systems continuously depending on a parameter, the set of lower semicontinuous points and the set of upper semicontinuous points of the \(\varepsilon \)-capacity of its systems considered a function of the parameter are described. For the set of upper semicontinuous points, this description is complete if the parameter belongs to a complete metric separable zero-dimensional space.
MSC:
| 37B55 | Topological dynamics of nonautonomous systems |
| 26A21 | Classification of real functions; Baire classification of sets and functions |
References:
| [1] | Kolmogorov, A. N., Asymptotic characteristics of totally bounded metric spaces, Dokl. Akad. Nauk SSSR, 179, 585-589 (1956) |
| [2] | Kolyada, S.; Snoha, L., Topological entropy of nonautonomous dynamical systems, Random Comput. Dyn., 4, 205-233 (1996) · Zbl 0909.54012 |
| [3] | Vetokhin, A. N., The exact baire class of topological entropy of nonautonomous dynamical systems, Math. Notes, 106, 327-333 (2019) · Zbl 1430.37017 · doi:10.1134/S0001434619090025 |
| [4] | Vetokhin, A. N., Topological entropy of a continuous family of smooth time-varying dynamical systems on an interval does not belong to the second Baire class, Differ. Equations, 56, 131-134 (2020) · Zbl 1444.37036 · doi:10.1134/S0012266120010140 |
| [5] | F. Hausdorff, Mengenlehre, 2nd ed. (de Gruyter, Berlin, 1927). · JFM 53.0169.01 |
| [6] | Kuratowski, K., Topologie (1933), Warsaw: Druk. M. Garasiński, Warsaw · JFM 59.0563.02 |
| [7] | Vetokhin, A. N., On some properties of topological entropy and topological pressure of families of dynamical systems continuously depending on a parameter, Differ. Equations, 55, 1275-1283 (2019) · Zbl 1439.37018 · doi:10.1134/S0012266119100021 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
