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2109.08953

Commuting Functions in Class K and Families of Wandering Baker Domains.

Adrián Esparza Amador

correctmedium confidence
Category
Not specified
Journal tier
Specialist/Solid
Processed
Sep 28, 2025, 12:56 AM

Audit review

The paper’s Theorem A states that if f,g ∈ K commute and f = g + c, then F(f) = F(g) and J(f) = J(g), and provides a two-case normality argument adapted to class K (with multiple essential singularities) to prove it . The candidate solution proves the same result by deriving the functional identity f^n = g^n + n c on suitable domains and transferring normality via divergence to ∞. This is a valid alternative route provided one carefully handles the domain-of-definition issues in class K; these details are briefly noted but could be made more explicit. Thus both are correct, with different proof styles.

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} specialist/solid

\textbf{Justification:}

The manuscript establishes equality of Julia/Fatou sets for commuting maps in class K under an additive relation, extending a classical result from the entire case, and leverages it to construct wandering Baker domains. The proof is concise and essentially correct, with small places where additional detail would enhance readability (critical point treatment, explicit normality criterion). The contribution is solid within transcendental dynamics.