2411.08317
ON REGULAR HÉNON-LIKE RENORMALIZATION
Jonguk Yang
correctmedium confidence
- Category
- Not specified
- Journal tier
- Strong Field
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper’s Theorem A (items (i)–(v)) and supporting propositions establish precisely the conclusions claimed; the model’s solution follows the same overall strategy: convergence of centered straightening charts, super-exponentially small vertical coupling (thinness), quadratic box geometry with bounded-type scaling, uniform Cr bounds, and exponential shadowing by 1D renormalization. The steps match the paper’s proofs and use the same key mechanisms (regular returns, a priori bounds, thinness, and 1D hyperbolicity).
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} strong field
\textbf{Justification:}
The manuscript presents a coherent, technically solid, and conceptually clear renormalization theory for dissipative Hénon-like maps of bounded combinatorics, incorporating Pesin-theoretic control to obtain a priori bounds and then deriving convergence and structural results (Theorem A, D, E). The arguments are detailed and consistent, and the main conclusions are significant for the 2D nonuniformly hyperbolic setting. Minor suggestions could further improve readability and traceability of certain constants and definitions.