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
- arXiv Links
- Abstract ↗PDF ↗
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.