Classical Hénon

We have a paper detailing the algorithmic approach and the results when applied to the Hénon map, at the classical parameter values:

Algorithms for rigorous entropy bounds and symbolic dynamics, S. Day, R. Frongillo and R. Trevino, submitted for publication, 2007.

Below is the image of the index pair for the main result, followed by the abstract of the paper.

The aim of this paper is to introduce a method for computing rigorous lower bounds for topological entropy. topological entropy. The topological entropy for a dynamical system measures the number of trajectories that separate in finite time and quantifies the complexity of the system. Our method relies on extending existing computational Conley index techniques for constructing semi-conjugate symbolic dynamical systems. Besides offering a description of the dynamics, the constructed symbol system allows for the computation of a lower bound for the topological entropy of the original system. Our overall goal is to construct symbolic dynamics that yield a high lower bound for entropy. The method described in this paper is algorithmic and, although it is computational, yields mathematically rigorous results. For illustration, we apply the method to the Hénon map, where we compute a rigorous lower bound for topological entropy of 0.4318.