Author

Ru-Xi Shi

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Preprint Sep 2026

A new type of deterministic Salem sets and its spectrality

For all $0<s \le 1$, we provide a new deterministic construction of Cantor sets whose Fourier dimension and Hausdorff dimension are both equal to $s$. The construction is based on a straightforward Cantor-Moran construction with contraction ratios given by reciprocals of integers. The key tool to obtain the fast Fourie...

Chun-Kit Lai, Ru-Xi Shi, Yu-Hao Xie · 2 citations · ⚡1

Preprint Sep 2026

A sharp embedding theorem for topological dynamical systems

Let $(X,T)$ be a topological dynamical system, and let $\dim(X,T)$ denote Meyerovitch's dynamical dimension. We prove that, for every integer $n\geq1$, if $\dim(X,T)<n/2$, then the set of maps $f\in C(X,[0,1]^n)$ for which the orbit map $$ I_f: X\longrightarrow([0,1]^n)^{\mathbb{Z}}, \qquad I_f(x)=\bigl(f(T^k x)\bigr)_...

Ru-Xi Shi · 1 citation