Recognition of motion is vitally important to any animal. Vision research has proposed a number of algorithms applicable to action recognition. However, unlike successes in early visual perception, the past studies have not yet established the computational theory of action recognition. In the present study, we employ a dynamical systems approach and hypothesize that motions are encoded cognitively as a topological structure abstracted from physical particulars. We investigated whether a common topological nature could be found in a type of rhythmic movement. The topological nature of action dynamics showed a striking similarity, which could not have been identified with other analyses where physical properties were retained. The result suggests that the dynamical perspective serves as a theoretical basis in studying complex human movements.