On rotated vector fields in higher-dimensional spaces (Q1813194)

A natural generalization of the concept of rotated vector fields in the plane is given to those in higher-dimensional spaces. Five related theorems are established. In three of them the limit surfaces with a certain special property are treated especially with respect to their absence in some rotated vector fields. Two concrete applications of the abstract results are introduced in \(\mathbb{R}^ 3\) to demonstrate the nonexistence of stable trajectories different from the singular point.