From template analysis to generating partitions II: Characterization of the symbolic encodings

Abstract

We give numerical evidence of the validity of a previously described algorithm for constructing symbolic encodings of chaotic attractors from a template analysis. We verify that the different solutions that can be found are dynamically equivalent, and that our approach yields results that are consistent with those obtained from methods based on homoclinic tangencies. This is further confirmed by verifying directly that the computed partitions are generating to a high degree of accuracy, and that they can be used to estimate precisely the metric entropy. It is also shown that the correct number of symbols needed to describe the dynamics is naturally provided, and that a compact parameterization of a partition can easily be determined, which makes our algorithm suitable for applications such as real-time encoding.