Author

Jian Wang

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Preprint Aug 2026

Quantitative Rigidity of pseudo-rotations on the two-torus and Sarnak's conjecture

We establish quantitative rigidity results for pseudo-rotations of the two-torus under a $(C,\delta)$-deviation condition relative to their rotation vectors. The main ingredient is a quantitative free-disk estimate that converts bounds on orbit deviation into explicit control of the distance between the iterates and th...

Yinshan Chang, Jian Wang, Jun-Chang Zhou · 1 citation

Preprint Aug 2026

Examples beyond Bounded Mean Motion for Quantitative Rigidity on the Two-Torus

This note supplies genuinely non-fibred examples for the manuscript: Rigidity on the Two-Torus and Sarnak's Conjecture. For every $0<\delta<\tfrac12$, we construct $C^\infty$ Lebesgue-area-preserving pseudo-rotations of $\mathbb{T}^2$ which satisfy the $(C,\delta)$-deviation condition but do not have bounded mean motio...

Yinshan Chang, Jian Wang, Jun-Chang Zhou · 1 citation

Preprint Aug 2026

Regularity, quantitative deviation, and non-rigidity of a lacunary skew product

Let $\alpha$ be irrational and let $q_j$ be the denominators of its continued-fraction convergents. We study the function \[ h(x)=\sum_{j\geq1}\frac{\cos(2\pi q_jx)}{q_j} \] and the skew product \[f(x,y)=(x+\alpha,y+h(x))\quad\mathrm{mod}\quad\mathbb{Z}^2.\] The function $h$ is H\"older continuous of every exponent bel...

Yinshan Chang, Jian Wang, Jun-Chang Zhou · 1 citation