3 papers
math-ph2025
Log-Hausdorff multifractality of the absolutely continuous spectral measure of the almost Mathieu operator
Jie Cao, Xianzhe Li, Baowei Wang +1
This paper focuses on the fractal characteristics of the absolutely continuous spectral measure of the subcritical almost Mathieu operator (AMO) and Diophantine frequency. In parti…
math.DS2025
Subordinacy theory for long-range operators: hyperbolic geodesic flow insights and monotonicity theory
Zhenfu Wang, Disheng Xu, Qi Zhou
We introduce a comprehensive framework for subordinacy theory applicable to long-range operators on , bridging dynamical systems and spectral analysis. For finit…
math.DS2025
Hyperbolicity for one-frequency analytic quasi-periodic (Hermitian)-symplectic cocycles
Duxiao Wang, Disheng Xu, Qi Zhou
We demonstrate the existence of an open dense subset within the class of real analytic one-frequency quasi-periodic $\mathrm{\Sp}(4,\mathbb{R})$-cocycles, characterized by either t…