2006.06786
Distinguished correlation properties of Chebyshev dynamical systems and their generalisations
Jin Yan, Christian Beck
correcthigh confidence
- Category
- Not specified
- Journal tier
- Specialist/Solid
- Processed
- Sep 28, 2025, 12:55 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper’s correlation formulas and the “minimum skeleton” claim are correct and well-supported by the Fourier/Diophantine selection rules. The model reproduces the Chebyshev (a=0) and general conjugacy formulas accurately, and its constructive strict-inclusion argument for r≥3 when extra harmonics are present is sound. However, the model’s assertion that for r=2 the nonzero-correlation index set is the same for all conjugacies is false: the paper explicitly shows off-diagonal two-point correlations for N-ary shift observables, whereas Chebyshev two-point correlations vanish off the diagonal, so S_cos(2) is strictly smaller in general.
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} specialist/solid
\textbf{Justification:}
The core results are correct and clearly motivated: the paper derives precise correlation selection rules for Chebyshev and general conjugate maps, and it persuasively argues that Chebyshev maps minimize the set of nonvanishing higher-order correlations. The exposition would benefit from a short formal argument to upgrade some "in general" statements to explicit set-inclusion claims, and from clarifying the exact assumptions on the conjugating function in the general case.