2509.01340
Chaos on Peano continua
Klára Karasová, Benjamin Vejnar
correctmedium confidence
- Category
- Not specified
- Journal tier
- Strong Field
- Processed
- Sep 28, 2025, 12:57 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper proves that every Peano continuum admits an exact Devaney chaotic self-map; the key statement is Theorem A (detailed in Theorem 10), whose proof builds a LEO map with dense periodic points via Lemma 4 and Lemma 9. The candidate solution explicitly invokes this main theorem and then notes that exactness implies transitivity, hence Devaney chaos—precisely the implication chain recorded in the paper. Thus, the model’s answer is a direct corollary of the paper’s main result rather than an independent proof; both are consistent and correct.
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} strong field
\textbf{Justification:}
The manuscript proves a broadly applicable and conceptually neat result: exact Devaney chaotic dynamics exists on every Peano continuum. The construction is careful and leverages locally constant-on-dense maps with refined perturbations to ensure both LEO and dense periodic points. The exposition is generally clear, though a few brief clarifications (noted below) would improve readability and self-containedness. The result advances the understanding of chaotic dynamics on continua.