Topological Entropy Bounds for Hyperbolic Plateaus of the H\'enon Map

Combining two existing rigorous computational methods, for verifying hyperbolicity (due to Arai) and for computing topological entropy bounds (due to Day et al.), we prove lower bounds on topological entropy for 43 hyperbolic plateaus of the H\'enon map. We also examine the 16 area-preserving plateaus studied by Arai and compare our results with related work. Along the way, we augment the algorithms of Day et al. with routines to optimize the algorithmic parameters and simplify the resulting semi-conjugate subshift.