Limits of Learning Dynamical Systems

The paper states Theorem 5.2 (Error from iterative forecast) precisely and supplies the needed definitions of the perturbed linear cocycle via \hat M and forcing c, together with the fluctuation set-up (5.16)–(5.17) and the reference dynamics, but it provides only a high-level sketch and a citation to prior work for proof details. The candidate solution reproduces the paper’s set-up exactly—linearizing \hat{\mathcal T} along the reference orbit t_n = (U^{n-1}\pi U\varphi, U^n\Phi), deriving the inhomogeneous linear recursion with \hat M and c, and then establishing (i) the second-order pointwise approximation and (ii) the L^2 growth bound on Pesin blocks at rate e^{n(\lambda_1+\varepsilon)}—matching equations (5.18)–(5.19). Thus the candidate’s derivation is correct and aligns with the stated result, while the PDF does not include the full proof. See the theorem statement and surrounding set-up in the PDF for the precise definitions of fluctuations, \hat M, c, and the comparison orbit (5.13)–(5.17) and Theorem 5.2 itself . The semi-conjugacy identity \mathcal T\circ h=h\circ f used by the model appears in the paper’s commutation diagram (2.5) .