Minimal Braid in Applied Symbolic Dynamics

Based on the minimal braid assumption, three-dimensional periodic flows of a dynamical system are reconstructed in the case of unimodal map, and their topological structures are compared with those of the periodic orbits of the Rössler system in phase space through the numerical experiment. The numerical results justify the validity of the minimal braid assumption which provides a suspension from one-dimensional symbolic dynamics in the Poincaré section to the knots of three-dimensional periodic flows.