Robust Devaney chaos in the two-dimensional border-collision normal form.

The paper proves Devaney chaos for the 2D border-collision normal form under ξ ∈ ΦBYG with J1(ξ) > 1 and J2(ξ) < 1 by an invariant-cone/expanding-line-segment method and a triangular trapping region Δ̃, culminating in Theorem 2.2. It does not claim a global Markov partition nor a conjugacy to the full two-shift. The candidate solution instead asserts a Smale–Birkhoff horseshoe on a curvilinear rectangle with a topological conjugacy to Σ2 and identifies K with Λ. These stronger claims are unproven in the candidate’s outline and contradict the paper’s more nuanced geometric construction (via Δ̃) and its avoidance of a full-shift conjugacy claim. Key steps in the candidate argument (two full-width strips for f(R) ∩ R from φ(ξ) > 0; preservation of spanning arcs from J1 > 1; uniform graph-transform contraction from J2 < 1; equality K = Λ) are not established in the paper and require additional nontrivial geometry. Thus, while both target Devaney chaos, the paper’s proof is correct as stated, and the model’s stronger claims are unsupported.