Topological Entropy of Generalized Bunimovisch Stadium Billiards

The paper proves liminf_{ℓ→∞} h_top(T_ℓ) ≥ log(1+√2) by constructing a finite-state coding on a compact invariant set K_{ℓ,N}, computing the spectral radius via the rome method, and letting N→∞; the candidate instead builds a uniform topological horseshoe for large ℓ using a large-slope estimate after unfolding and obtains the same lower bound via a 3×3 transition matrix. Both arguments are logically sound for the stated goal; the model’s proof is geometrically different and somewhat stronger on its face (claiming a uniform bound for all sufficiently large ℓ), which likely requires extra uniformity checks. For the liminf bound, both are correct.