A filtered Hénon map

Vinícius S. Borges, Marcio Eisencraft

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Category: Not specified
Journal tier: Specialist/Solid
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper correctly defines the filtered Hénon map, derives the fixed-point formulas, the Jacobian, and uses the spectral-radius criterion for linear stability, but it (i) treats the existence of two fixed points as failing only at c0=c1=0 instead of on the whole line c0+c1=0, and (ii) states the instability of P1 and the stability region of P2 purely from numerics. The candidate solution provides complete analytic arguments: a clean proof that P1 is always unstable (when c0+c1≠0), a compact Jury/Schur characterization of the P2-stability region, and a correct implication that h<0 on the basin of a stable P2. These reconcile with and strengthen the paper’s numerical findings.

Referee report (LaTeX)

\textbf{Recommendation:} major revisions

\textbf{Journal Tier:} specialist/solid

\textbf{Justification:}

The paper addresses a pertinent variation of the Hénon map and provides thorough numerical explorations of stability and Lyapunov exponents. However, two key claims (that P1 is always unstable and the delineation of the P2-stability region) are left at the numerical level though they admit short, standard analytic proofs. There is also a minor but real misstatement about the fixed-point count on the line c0 + c1 = 0. Rectifying these issues would significantly strengthen the work’s rigor without altering its main conclusions.