Knotted Periodic Solutions of a Linear Nonautonomous System and Some Related Three-Dimensional Flows

Abstract

This paper considers a three-dimensional linear nonautonomous systems. It shows that for every integer frequency parameter value, this system has a distinct type of knotted periodic solutions, which lie in a bounded region of R 3 . Exact explicit parametric representations of the knotted periodic solutions are given. By using these parametric representations, two series of threedimensional flows are constructed, such that these three-dimensional autonomous systems have knotted periodic orbits in the three-dimensional phase space.