2507.23731
Fourier decay of equilibrium states and the Fibonacci Hamiltonian
Gaétan Leclerc
correctmedium confidence
- Category
- math.DS
- Journal tier
- Strong Field
- Processed
- Sep 28, 2025, 12:57 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper proves exactly the claimed statement for area-preserving Axiom A diffeomorphisms on surfaces: under non-C2 of Es or Eu on a basic set, the measure of maximal entropy has positive lower Fourier dimension in C1+α (Theorem 1.4), by reducing Fourier decay to a Quantitative Nonlinearity (QNL) condition (Definition 3.1, Theorem 3.1) and then verifying QNL via oscillations of the temporal distance function using Tsujii–Zhang–type arguments; the area-preserving hypothesis extends decay to arbitrary C1+α chart phases (Corollary 3.2). The model’s solution follows the same reduction (Theorem 3.1), the same use of nonlinearity to get QNL, and the same area-preserving extension (Cor. 3.2), culminating in the same conclusion (Theorem 1.4). Hence both are correct and use substantially the same proof architecture .
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} strong field
\textbf{Justification:}
The work delivers a substantive advance: polynomial Fourier decay (hence positive lower Fourier dimension) for equilibrium states in a broad Axiom A, area-preserving, nonlinear setting, and a compelling application to the Fibonacci Hamiltonian. The proof architecture—sum–product reduction to QNL, verification of QNL via temporal-distance oscillations and templates, and an area-preserving extension—is well executed. Minor revisions would increase self-containment and polish (uniform range for α, sketching cited steps).