Necessary and sufficient conditions for topological equivalence of three-dimensional Morse–Smale dynamical systems with a finite number of singular trajectories

The author introduces a complete topological invariant of three-dimensional Morse–Smale systems with finitely many singular trajectories, including closed trajectories, which is called the scheme of the dynamical system. Conditions for the equivalence of schemes are given, and it is shown that two systems are topological equivalent if and only if their schemes are equivalent.