Zobrazeno 1 - 10
of 88
pro vyhledávání: '"Shi, Ruxi"'
Autor:
Shi, Ruxi, Zhang, Guohua
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 Burguet and the first-named author of the paper.
Comment: 16 pages
Comment: 16 pages
Externí odkaz:
http://arxiv.org/abs/2308.03270
Autor:
Burguet, David, Shi, Ruxi
We define the topological multiplicity of an invertible topological system $(X,T)$ as the minimal number $k$ of real continuous functions $f_1,\cdots, f_k$ such that the functions $f_i\circ T^n$, $n\in\mathbb Z$, $1\leq i\leq k,$ span a dense linear
Externí odkaz:
http://arxiv.org/abs/2307.08906
Autor:
Shi, Ruxi, Tsukamoto, Masaki
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 continuous maps between dynamical systems and assume that the mean dimension o
Externí odkaz:
http://arxiv.org/abs/2211.10158
Autor:
Gutman, Yonatan, Shi, Ruxi
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 enables us to answer positively a question of Bowen and Walters from
Externí odkaz:
http://arxiv.org/abs/2206.12308
Autor:
Burguet, David, Shi, Ruxi
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 infinite topological mean dimension. We also estimate the rate of divergence
Externí odkaz:
http://arxiv.org/abs/2206.10508
Autor:
Liang, Bingbing, Shi, Ruxi
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 metrizable abelian group. As an application, we obtain that the mean dimensio
Externí odkaz:
http://arxiv.org/abs/2203.01122
Let $\{s_n\}_{n\in\N}$ be a decreasing nonsummable sequence of positive reals. In this paper, we investigate the weighted Birkhoff average $\frac{1}{S_n}\sum_{k=0}^{n-1}s_k\phi(T^kx)$ on aperiodic irreducible subshift of finite type $\Sigma_{\bf A}$
Externí odkaz:
http://arxiv.org/abs/2109.03898
Autor:
Burguet, David, Shi, Ruxi
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 zero-dimensional flow. Following [Bur19] we deduce that any topologic
Externí odkaz:
http://arxiv.org/abs/2105.09732
Autor:
Burguet, David, Shi, Ruxi
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) strongly permutative, permutative algebraic and unit one-dimensional auto
Externí odkaz:
http://arxiv.org/abs/2105.09708
Autor:
Shi, Ruxi, Tsukamoto, Masaki
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 this index theory and topological dynamics. Given a fixed-point free dy
Externí odkaz:
http://arxiv.org/abs/2103.11654