Counterexamples to the Seifert conjecture
Summary: Since H. Seifert proved in 1950 the existence of a periodic orbit for a vector field on the 3-dimensional sphere \(S^3\) which forms small angles with the fibers of the Hopf fibration, several examples of aperiodic vector fields on \(S^3\) have been produced as well as results showing that in some situations a compact orbit must exist. This paper surveys presently known types of vector fields without periodic orbits on \(S^3\) and on other manifolds.
scientific article; zbMATH DE number 1184292