Unstable periodic orbits and templates of the Rössler system: Toward a systematic topological characterization

The Rössler system has been exhaustively studied for parameter values (a∈[0.33,0.557],b=2,c=4). Periodic orbits have been systematically extracted from Poincaré maps and the following problems have been addressed: (i) all low order periodic orbits are extracted, (ii) encoding of periodic orbits by symbolic dynamics (from 2 letters up to 11 letters) is achieved, (iii) some rules of growth and of pruning of the periodic orbits population are obtained, and (iv) the templates of the attractors are elaborated to characterize the attractors topology.