Sakata, Sadahisa; Hara, Tadayuki Dynamics of a linear differential system with piecewise constant argument. (English) Zbl 0976.34062 Dyn. Contin. Discrete Impulsive Syst. 7, No. 4, 585-594 (2000). The authors study the dynamics of a linear differential system with piecewise constant argument \((L)\) \(\dot x(t)=-\alpha R(\theta)x([t])\), with \(\alpha>0\) and \(R(\theta)= \left(\begin{smallmatrix}\cos\theta &-\sin\theta\\ \sin\theta &\cos\theta\end{smallmatrix}\right)\) with \(|\theta |< \frac{\pi}2\). In case \(\alpha =2\cos \theta \), it is shown that there exist star-shaped periodic solutions to (L) if \(\frac\theta\pi\in Q\) and any nontrivial trajectory \(x(t)\) to (L) is everywhere dense on some closed annular region if \(\frac{\theta }{\pi} \notin Q\). It is also proved that any solution to (L) converges to \(0\) as \(t\to \infty\) if and only if \(\alpha<2\cos\theta \). Reviewer: Yuan Rong (Beijing) Cited in 3 Documents MSC: 34K13 Periodic solutions to functional-differential equations Keywords:periodic solution; everywhere dense; linear system PDFBibTeX XMLCite \textit{S. Sakata} and \textit{T. Hara}, Dyn. Contin. Discrete Impulsive Syst. 7, No. 4, 585--594 (2000; Zbl 0976.34062)