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math.DS2026
Monotonicity, global symplectification and the stability of Dry Ten Martini Problem
Xianzhe Li, Disheng Xu, Qi Zhou
For any fixed irrational frequency and trigonometric-polynomial potential, we show that every type I energy with positive Lyapunov exponent that satisfies the gap-labelling conditi…
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…