Abstract
One of the important directions of the qualitative theory of ordinary differential equations is to study the properties of linear systems that satisfy the condition of integral separation. Anyway, integral separation becomes apparent in all studies concerning the asymptotic behavior of the solutions for the linear systems under the action of small perturbations.The papers of V.M. Millionschikov, B.F. Bylov, N.A. Izobov, I.N. Sergeev et al. proved that the available integral separation is the main reason for the rough stability of the characteristic Lyapunov exponents, the rough stability of the highest Lyapunov exponent, and the rough diagonalizability of systems by Lyapunov transformations, and other fundamental properties of linear differential systems.The paper presents the basic properties of the set of linear systems with constant, periodic, reducible coefficients and proves the algebraic criteria for their property of integral separation of solutions to be available.The results can be used in modeling dynamic processes.
Highlights
 ñòàòüå èññëåäóþòñÿ ëèíåéíûå äèôôåðåíöèàëüíûå ñèñòåìû, óäîâëåòâîðÿþùèå óñëîâèþ èíòåãðàëüíîé ðàçäåëåííîñòè ðåøåíèé
 íàñòîÿùåé ðàáîòå áóäåò ïðèâåäåí ðÿä îñíîâíûõ ïîíÿòèé è ôóíäàìåíòàëüíûõ ñâîéñòâ ìíîæåñòâ LS è T
Ìèëëèîíùèêîâ Â.Ì.Ñèñòåìû ñ èíòåãðàëüíîé ðàçäåëåííîñòüþ âñþäó ïëîòíû â ìíîæåñòâå âñåõ ëèíåéíûõ ñèñòåì äèôôåðåíöèàëüíûõ óðàâíåíèé // Äèôôåðåíöèàëüíûå óðàâíåíèÿ
Summary
 ñòàòüå èññëåäóþòñÿ ëèíåéíûå äèôôåðåíöèàëüíûå ñèñòåìû, óäîâëåòâîðÿþùèå óñëîâèþ èíòåãðàëüíîé ðàçäåëåííîñòè ðåøåíèé. Ñåðãååâà [7, 8], K.J. Palmer [9] óñòàíîâëåíî, ÷òî íàëè÷èå ñâîéñòâà èíòåãðàëüíîé ðàçäåëåííîñòè ÿâëÿåòñÿ ãëàâíîé ïðè÷èíîé óñòîé÷èâîñòè õàðàêòåðèñòè÷åñêèõ ïîêàçàòåëåé Ëÿïóíîâà è ðàçëè÷íûõ àñèìïòîòè÷åñêèõ ñâîéñòâ ëèíåéíûõ äèôôåðåíöèàëüíûõ ñèñòåì. Óñëîâèå (3) ïîêàçûâàåò, ÷òî ëèíåéíûå ñèñòåìû ñî ñâîéñòâîì èíòåãðàëüíîé ðàçäåëåííîñòè ÿâëÿþòñÿ òèïè÷íûìè ïðåäñòàâèòåëÿìè ëèíåéíûõ ñèñòåì îáûêíîâåííûõ äèôôåðåíöèàëüíûõ óðàâíåíèé â ïðîñòðàíñòâå LS.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
