2209.04905
HETEROCHAOS BAKER MAPS AND THE DYCK SYSTEM: MAXIMAL ENTROPY MEASURES AND A MECHANISM FOR THE BREAKDOWN OF ENTROPY APPROACHABILITY
Hiroki Takahasi, Kenichiro Yamamoto
correcthigh confidence
- Category
- Not specified
- Journal tier
- Strong Field
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper proves existence and (ergodic) uniqueness of two measures of maximal entropy for the generalized heterochaos baker maps by coding to the Dyck shift and by a careful entropy upper bound via Lyapunov exponents. The candidate solution instead posits a principal extension to the one-dimensional base map F_a and constructs supposed Dirac-fiber “principal lifts.” This conflicts with the paper’s non-injective coding and full-support MMEs, misuses principality, and contains a concrete error in the z-coordinate series. Hence the paper’s argument is correct, while the model’s proof is flawed.
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} strong field
\textbf{Justification:}
The manuscript establishes a natural coding of generalized heterochaos baker maps by the Dyck system and leverages this to prove the existence of two ergodic Bernoulli MMEs and a clean entropy upper bound for all measures. The methods are original in this context and technically sound. Minor editorial improvements would further clarify the Lyapunov-based entropy bound and the non-injectivity of the coding.