RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Tr. Inst. Mat.: Year: Volume: Issue: Page: Find

 Tr. Inst. Mat., 2010, Volume 18, Number 2, Pages 93–98 (Mi timb21)

On simple linear differential systems with an even matrix

E. V. Musafirov

Polesskiy State University

Abstract: Conditions of simplicity of linear differential systems with an even coefficient matrix are obtained. Fundamental matrixes of solutions of linear differential systems $\dot{x}=2P(t)x$ and $\dot{x}=-2P(-t)x$ are expressed by means of reflective matrix $F(t)$ of simple system $\dot{x}=P(t)x$, $t\in\mathbb{R}$, $x\in\mathbb{R}^n$. Fundamental matrixes of solutions of systems $\dot{x}=-2kP(t)x$, $k\in\mathbb{Z}$ and $\dot{x}=-2P(t)x+\dot{P}(t)P^{-1}(t)x$ are also expressed by means of $F(t)$ under condition of evenness of matrix $P(t)$. Equivalence (in terms of coincidence of reflective functions) of last system and a simple system $\dot{x}=-2P(t)x$ with an even coefficient matrix is proved.

Full text: PDF file (199 kB)
References: PDF file   HTML file

Bibliographic databases:
UDC: 517.926.7

Citation: E. V. Musafirov, “On simple linear differential systems with an even matrix”, Tr. Inst. Mat., 18:2 (2010), 93–98

Citation in format AMSBIB
\Bibitem{Mus10} \by E.~V.~Musafirov \paper On simple linear differential systems with an even matrix \jour Tr. Inst. Mat. \yr 2010 \vol 18 \issue 2 \pages 93--98 \mathnet{http://mi.mathnet.ru/timb21} \zmath{https://zbmath.org/?q=an:05863494}