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Perturbations of dynamical systems on simple time scales. / Pilyugin, S. Yu. .
в: Lobachevskii Journal of Mathematics, Том 44, № 3, 03.2023, стр. 1215-1222.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - Perturbations of dynamical systems on simple time scales
AU - Pilyugin, S. Yu.
PY - 2023/3
Y1 - 2023/3
N2 - We study perturbations of dynamical systems in Banach spaces for which time varieson simple time scales consisting of families of isolated segments of the real axis. On a segment of the time scale, the system is governed by an ordinary differential equation; the transfer of a trajectory from a segment to the next one is determined by a map of the Banach space. The main problem which we study is the following one: given a trajectory of the original system, can we find a close trajectory of a perturbed system? We study perturbations applying the so-called multiscale approach: it is assumed that there exists a countable family of projections of the phase space and the smallnessconditions are imposed on the projections of perturbations. To find a solution close to a specified solution of the unperturbed system, we introduce a generalization of the Perron method.
AB - We study perturbations of dynamical systems in Banach spaces for which time varieson simple time scales consisting of families of isolated segments of the real axis. On a segment of the time scale, the system is governed by an ordinary differential equation; the transfer of a trajectory from a segment to the next one is determined by a map of the Banach space. The main problem which we study is the following one: given a trajectory of the original system, can we find a close trajectory of a perturbed system? We study perturbations applying the so-called multiscale approach: it is assumed that there exists a countable family of projections of the phase space and the smallnessconditions are imposed on the projections of perturbations. To find a solution close to a specified solution of the unperturbed system, we introduce a generalization of the Perron method.
KW - system on time scale
KW - perturbation
KW - Perron operator
KW - multiscale approach
M3 - Article
VL - 44
SP - 1215
EP - 1222
JO - Lobachevskii Journal of Mathematics
JF - Lobachevskii Journal of Mathematics
SN - 1995-0802
IS - 3
ER -
ID: 105345532