Zhiqiang Wang

activity

20242026

collaborators

7 papers

math.DS2026

Self-similarity of unions of self-similar sets and their translations

Zhiqiang Wang

In this paper, we explore the self-similarity of unions of self-similar sets and their translations. For $N \in N$ and $0 < I^^{2} < 1/ (N + 1)$ , let $I^$ be the self-similar set g…

math.CA2025

On infinite scalings of the canonical spectrum for self-similar spectral measures

Zhiqiang Wang

Let $(I^¼, I^)$ be the canonical spectral pair generated by a Hadamard triple $(N, B, L)$ in $R$ with $0 \in B \cap L$ , which means that the family $\big\{ e_Î»(x)=e^{2Ï\math…

math.DS2025

Open dynamical systems with a moving hole

Derong Kong, Beibei Sun, Zhiqiang Wang

Given an integer $b \geq 3$ , let $T_{b} : [0, 1) \to [0, 1); x \mapsto b x (mod 1)$ be the expanding map on the unit circle. For any $m \in N$ and $Ï=Ï^0Ï^1\ldots\in(\left\{0,1,\ldo…

math.DS2025

Self-embeddings of homogeneous self-similar sets generated by three maps

Zhiqiang Wang

For $0 < I ¨ < 1/3$ and $I ¨ \leq I^» \leq 1 - 2 I ¨ $ , let $E$ be the self-similar set generated by the iterated function system $$Î¦= \big\{ Ï_1(x) = Ïx ,\; Ï_2(x) = Ïx + Î», \; Ï_3(x) =…

math.DS2025

On the reducibility of the 1d quantum harmonic oscillator with a quasi-periodic bounded potential

Emanuele Haus, Zhiqiang Wang

Using the decay along the diagonal of the matrix representing the perturbation with respect to the Hermite basis, we prove a reducibility result in $L^{2} (R)$ for the one-di…

math.CA2025

On the intersection of Cantor set with the unit circle and some sequences

Kan Jiang, Derong Kong, Wenxia Li +1

For $I^» \in (0, 1/2)$ let $K_{I^} »$ be the self-similar set in $R$ generated by the iterated function system ${f_{0} (x) = I^» x, f_{1} (x) = I^» x + 1 - I^»}$ . In this paper, we investigate the…