EFFICIENT COMPUTATION OF STATISTICAL PROPERTIES OF INTERMITTENT DYNAMICS

The candidate solution establishes (i) the Abel representation of the first return map and return time formulas exactly as in Theorem 2.1 (equations (4)–(6)) and (ii) the existence of a principal Abel function with the inverse-iterate limit (7), analytic extension to a half-strip, an explicit asymptotic expansion, and a quantitative remainder bound as in Theorem 2.2 (equation (8) with constants detailed around (24)). The paper’s proof proceeds via a conjugation to z = x^α and Szekeres’ regular iteration framework, while the model’s proof uses a direct matched-asymptotic and discrete Green-series approach; these are different but compatible arguments. Note: the main-theorem statement’s error term appears with a sign that would contradict asymptoticity if interpreted literally; the body of the proof (see the bound derived from (24)) makes clear the remainder decays with |z|, matching the model’s bound. Overall, both are correct; the paper would benefit from clarifying this minor typographical issue.