Existence of an attractor and Horseshoe in multidimensional Hénon map

The paper’s general approach via auxiliary 1‑D envelopes and the Manhattan norm is sound, and the cubic-case bounds match the model. However, in the quadratic case the printed parameter restriction in Theorem 2 is inconsistent with the paper’s own derivation; inserting γ = α|b|/(1−a) and α = μ + γ into (μ+γ)^2 < 2μ yields μ < 2((1−a−|b|)/(1−a))^2, not μ < 2((1−|b|)/(1−a))^2. The horseshoe proof is also too sketchy (no covering/cone verification or y-bounds tied to Dx), whereas the model provides a standard strip/covering construction and corrects the quadratic bound. Overall, the model’s solution is correct and more complete on the critical points.