3 papers
math.SP2026
Transfer Operators, Canonical Center Dynamics, and Spectral Applications for Long-Range Operators
Xianzhe Li, Zhenfu Wang, Jiangong You +1
We introduce an operator-theoretic framework for long-range operators over general dynamical systems with analytic hopping and small potential. By establishing a partially hyperbol…
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-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…