21 citations · 43 across the 29 of their papers we have counts for
30 papers
A new type of deterministic Salem sets and its spectrality
Chun-Kit Lai, Ruxi Shi, Yu-Hao Xie
For all , we provide a new deterministic construction of Cantor sets whose Fourier dimension and Hausdorff dimension are both equal to . The construction is based on…
Dynamical dimension and shift embeddability without the marker property
Ruxi Shi
We study the aperiodic inverse-limit system constructed in our earlier work as an example of a finite-mean-dimensional dynamical system without the marker property. We prove that i…
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…
Mean topological dimension of induced amenable group actions
Ruxi Shi, Guohua Zhang
In this paper we generalize [BS22, Main Theorem] from actions of a single transformation to amenable group actions, which answers affirmatively the question raised in [BS22] by Bur…
Multiplicity of topological systems
David Burguet, Ruxi Shi
We define the topological multiplicity of an invertible topological system as the minimal number of real continuous functions such that the functions…
Application of waist inequality to entropy and mean dimension
Ruxi Shi, Masaki Tsukamoto
Waist inequality is a fundamental inequality in geometry and topology. We apply it to the study of entropy and mean dimension of dynamical systems. We consider equivariant continuo…
Topological mean dimension of induced systems
David Burguet, Ruxi Shi
For a topological system with positive topological entropy, we show that the induced transformation on the set of probability measures endowed with the weak- topology has infini…
Strongly isomorphic symbolic extensions for expansive topological flows
Yonatan Gutman, Ruxi Shi
In this paper, we prove that finite-dimensional topological flows without fixed points and having a countable number of periodic orbits, have the small flow boundary property. This…
Mean dimension of natural extension of algebraic systems
Bingbing Liang, Ruxi Shi
Mean dimension may decrease after taking the natural extension. In this paper we show that mean dimension is preserved by natural extension for an endomorphism on a compact metriza…
Spectrum of weighted Birkhoff average
Balázs Bárány, Michał Rams, Ruxi Shi
Let be a decreasing nonsummable sequence of positive reals. In this paper, we investigate the weighted Birkhoff average …
Zero-dimensional and symbolic extensions of topological flows
David Burguet, Ruxi Shi
A zero-dimensional (resp. symbolic) flow is a suspension flow over a zero-dimensional system (resp. a subshift). We show that any topological flow admits a principal extension by a…
Mean dimension of continuous cellular automata
David Burguet, Ruxi Shi
We investigate the mean dimension of a cellular automaton (CA for short) with a compact non-discrete space of states. A formula for the mean dimension is established for (near) str…
Divergent coindex sequence for dynamical systems
Ruxi Shi, Masaki Tsukamoto
When a finite group freely acts on a topological space, we can define its index and coindex. They roughly measure the size of the given action. We explore the interaction between t…
Finite mean dimesnion and marker property
Ruxi Shi
In this paper, we develop the theory of -index which has been introduced by Tsukamoto, Tsutaya and Yoshinaga. As an application, we show that given any positive numbe…
On variational principles for metric mean dimension
Ruxi Shi
In this note, we show several variational principles for metric mean dimension. First we prove a variational principles in terms of Shapira's entropy related to finite open covers.…
Embedding theorems for discrete dynamical systems and topological flows
Ruxi Shi
In this paper, we investigate the embeddings for topological flows. We prove an embedding theorem for discrete topological system. Our results apply to suspension flows via constan…
On the multifractal spectrum of weighted Birkhoff averages
Balázs Bárány, Michał Rams, Ruxi Shi
In this paper, we study the topological spectrum of weighted Birkhoff averages over aperiodic and irreducible subshifts of finite type. We show that for a uniformly continuous fami…
On -adic spectral measures
Ruxi Shi
A Borel probability measure on a locally compact group is called a spectral measure if there exists a subset of continuous group characters which forms an orthogonal basis of t…
A counter-example for polynomial version of Sarnak's conjecture
Zhengxing Lian, Ruxi Shi
We construct the counter-example for polynomial version of Sarnak's conjecture for minimal systems, which assets that the Möbius function is linearly disjoint from subsequences alo…
On dimensions of frame spectral measures and their frame spectra
Ruxi Shi
In this paper, we prove that the entropy dimension of a frame spectral measure is superior than or equal to the Beurling dimension of its frame spectrum.