A dynamical system on \(R^ 3\) with uniformly bounded trajectories and no compact trajectories. (English) Zbl 0676.58047

Kuperberg, K. M.; Reed, Coke S.

Proc. Am. Math. Soc. 106, No. 4, 1095-1097 (1989).

Summary: This paper contains an example of a rest point free dynamical system on \(R^ 3\) with uniformly bounded trajectories, and with no circular trajectories. The construction is based on an example of a dynamical system described by P. A. Schweitzer, and on an example of a dynamical system on \(R^ 3\) constructed previously by the authors.

MSC:

37C10	Dynamics induced by flows and semiflows
54H20	Topological dynamics (MSC2010)

Keywords:

rest point free dynamical system; uniformly bounded trajectories