Stepsize Variations for Lyapunov Exponents to Counter Persistent Errors

The paper proves convergence of Benettin’s algorithm with varying stepsizes under explicit assumptions, notably strong fast invertibility (FI) at the relevant index L, and derives the multi-exponent result via exterior powers, with the key algebraic QR–exterior-power identity and a relative global error bound that is uniform in N (Eqs. (15)–(16)), obtained using a discrete Gronwall-type argument and FI; see Theorem 5.2, Lemma 5.7(viii)–(ix), and the reduction via exterior powers . The model’s proof sketches the same high-level pathway but (i) drops the (FI)Lstrong hypothesis that the paper requires, and (ii) asserts a per-step multiplicative comparison that yields a uniform-in-N bound for the ratio of numerical and exact L-volume gains, without addressing noncommutativity or the conjugation effects of partial products. This key step is unsubstantiated and, absent FI or an equivalent domination/gap condition, is not justified. Hence, while the conclusion matches the paper’s theorem, the model’s argument is incomplete/incorrect at a crucial step.