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JOURNALS // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika // Archive

Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2020 Number 6, Pages 19–26 (Mi vmumm4361)

Mathematics

Structure of sets of semicontinuous points of $\varepsilon$-capacity of non-autonomous dynamical systems continuously depending on a parameter

A. N. Vetokhinab

a Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b Bauman Moscow Higher Technical School

Abstract: For a family of non-autonomous dynamical systems continuously depending on a parameter, we present descriptions of the set of lower semicontinuity points and the set of upper semicontinuity points of the $\varepsilon$-capacity of its systems considered as a function of the parameter. For the set of points of upper semicontinuity, this description is complete if the parameter belongs to a complete metric separable zero-dimensional space.

Key words: $\varepsilon$-capacity, non-autonomous dynamical system, Baire classification of functions.

UDC: 517.93

Received: 07.02.2020


 English version:
Moscow University Mathematics Bulletin, Moscow University Mеchanics Bulletin, 2020, 75:6, 246–252

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© Steklov Math. Inst. of RAS, 2025