Entropy estimation of the Hénon attractor

The topological entropy of the Hénon attractor is estimated using a function that describes the stable and unstable manifolds of the Hénon map. This function provides an accurate estimate of the length of curves in the attractor. The estimation method presented here can be applied to cases in which the invariant set is not hyperbolic. From the result of the length calculation, we have estimated the topological entropy h as h ∼ 0.49703 for the original parameters a = 1.4 and b = 0.3 adopted by Hénon.

► We estimate the topological entropy of the Hénon attractor. ► For the estimation, a function that describes the unstable manifold is used. ► The topological entropy is estimated by calculating the length of the curves. ► From the calculation result, the entropy h is estimated as h ⩾ 0.49703.