ITERATION PROBLEM FOR SEVERAL CHAOS IN NON-AUTONOMOUS DISCRETE SYSTEM

The paper asserts that Li–Yorke chaos is preserved under k-iterates provided the non-autonomous system f1,∞ merely converges to a map f (Theorem 1), but in the necessity proof it implicitly uses stability of finite compositions under pointwise convergence, specifically the step claiming lim_i f^ℓ_{kq_i+r+1}(x0) = f^ℓ(x0) without uniform convergence or an equicontinuity/N-convergence hypothesis, leaving a material gap in the argument (see the proof of Theorem 1 and the step following (3.1)–(3.2)) . The paper correctly defines the k-th iterate as the block system f[k]1,∞ := (f^k_{k(n−1)+1})n≥1 and contrasts it with uniform-convergence-based lemmas . By contrast, the model conflates the block iterate f[k]1,∞ with the sliding-window sequence (g_n = f^k_n), incorrectly claiming they have identical n-th iterates, and then appeals to a broad iterate-invariance theorem without the extra hypotheses (e.g., equicontinuity or N-convergence) that the paper itself points to as typically needed for such invariance results for related chaos notions . Consequently, both the paper’s proof (as written) and the model’s solution are incomplete.