From the 1 of 7 linked papers with an AI index.
7 papers
Dynamical dimension and shift embeddability without the marker property
Ruxi Shi
The paper computes the mean dimension and dynamical dimension of a specific aperiodic inverse‑limit system (both equal to N) and shows that, despite lacking the marker property, it…
Fuglede's conjecture holds for three intervals
Ruxi Shi
We prove that every bounded measurable subset of the real line that is both spectral and a union of three intervals tiles the line by translations, thereby completing Fuglede's con…
A variational principle for metric mean dimension via lower Brin-Katok local entropy
Ruxi Shi
We prove a finite-scale comparison between lower Brin-Katok local entropy and Katok covering entropy. Let be a compact metric topological dynamical system and l…
Spectra for finite unions of line segments
Mihail N. Kolountzakis, Ruxi Shi, Sha Wu
In this paper we study the spectrality of arc-length measures supported on the union of two line segments in the plane. We show that any such spectral measure must admit a line spe…
When is the fractal uncertainty principle for discrete Cantor sets most uncertain?
Chun-Kit Lai, Ruxi Shi
We give a necessary and sufficient condition to achieve the most uncertain exponent in the fractal uncertainty principle of discrete Cantor sets. The condition will be described as…
Lowering mean topological dimension
Ruxi Shi
In this paper, we prove that for a topological dynamical system with positive mean topological dimension and marker property, it has factors of arbitrary small mean topological dim…