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2102.09374

Interval maps generated by erasing block substitutions

A. Della Corte, M. Farotti

correctmedium confidence
Category
math.DS
Journal tier
Specialist/Solid
Processed
Sep 28, 2025, 12:56 AM

Audit review

The candidate solution reproduces, in essence, the paper’s constructions: it uses the same σ-gluing mechanism (Lemmas 4.2 and 4.5), derives dense orbits, 1/2-sensitivity, and dense periodic points (hence Devaney chaos), builds an uncountable scrambled set (Li–Yorke chaos), proves infinite topological entropy under lim |w|/ε(w) = ∞, and identifies an almost fixed point at x0 = 0.wε^∞. Minor overstatements in the candidate (e.g., claiming ≥1/2 separation in the Li–Yorke construction and “both” left/right accumulation at x0) go beyond what’s proved in the paper, but do not invalidate the main conclusions.

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} specialist/solid

\textbf{Justification:}

The work develops a coherent framework for interval maps generated by erasing block substitutions, with a clear hierarchy of erasing strength and sharp dynamical consequences. Proofs are sound and the main constructions (gluing, branching, spreading) are well tailored to the non-morphic setting. Exposition is generally clear, with minor opportunities to tighten quantitative statements and centralize technical conventions.