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Yini Yang

Publications and source records attributed to Yini Yang.

11 recordsLinked to original sources
arXiv2026

Weighted orbits of hypercyclic vectors on F-spaces

We study $\mathcal{F}$-hypercyclicity of weighted orbits $λ_nT^nx$ for continuous linear operators $T$ on complex F-spaces, where $\mathcal{F}$ is a Furstenberg family with the cut--shift--and--paste (CuSP) property. We characterize the scalar sequences for which weighted hypercyclicity always implies ordinary hypercyclicity: their nonzero values must be bounded and bounded away from zero. The same condition removes weights for every such family. For the converse inclusion, we prove that a bounded scalar sequence preserves all $\mathcal{F}$-hypercyclic vectors if its backward-shift $ω$-limit system is distal and does not contain the zero sequence. For chaotic operators, minimality of this system suffices. In particular, every complex nilsequence which is not identically zero preserves $\mathcal{F}$-hypercyclicity, and equality holds when its nonzero values are bounded away from zero. We also obtain simultaneous weighted return results and stability under unimodular weights with asymptotically trivial multiplicative differences.

math.FA↗
arXiv2026

Return Time Sets of Minimal Points for Countable Group Actions

For a countably infinite discrete group $G$, we study subsets of $G$ that contain a neighbourhood return-time set of a minimal point in a $G$-flow $X$. For $e\in F\subseteq G$, we characterize this property by the existence of $e\in A\subseteq F$ such that $\operatorname{Int}_K(A):=\{t\in G:Kt\subseteq A\}$ is right syndetic for every finite $K\subseteq A$, and equivalently by the support of a minimal binary configuration in the Bernoulli shift $2^G$. Additional conditions on $\operatorname{Int}_K(A) \operatorname{Int}_K(A)^{-1}$ characterize realization by minimal flows that are weakly mixing of all finite orders or strongly mixing: for every such $K$, the former requires that for each finite $H\subseteq G$ there is $c\in G$ with $HcH\subseteq \operatorname{Int}_K(A) \operatorname{Int}_K(A) ^{-1}$, whereas the latter requires that $\operatorname{Int}_K(A)\operatorname{Int}_K(A)^{-1}$ be cofinite. We also construct, for every compact metrizable minimal $G$-flow, a free minimal, strongly mixing Cantor flow disjoint from it.

math.DS↗
arXiv2026

Return time sets and product recurrence

Let $G$ be a countable infinite discrete group. We show that a subset $F$ of $G$ contains a return time set of some piecewise syndetic recurrent point $x$ in a compact Hausdorff space $X$ with a $G$-action if and only if $F$ is a quasi-central set. As an application, we show that if a nonempty closed subsemigroup $S$ of the Stone-Čech compactification $βG$ contains the smallest ideal $K(βG)$ of $βG$ then $S$-product recurrent is equivalent to distality, which partially answers a question of Auslander and Furstenberg (Trans. Amer. Math. Soc. 343, 1994, 221--232).

math.DS↗
arXiv2025

Distributionally chaotic $C_0$-semigroups on complex sectors

We explore distributional chaos for $C_0$-semigroups of linear operators on Banach spaces whose index set is a sector in the complex plane. We establish the relationship between distributional sensitivity and distributional chaos by characterizing them in terms of distributionally (semi-)irregular vectors. Additionally, we provide conditions under which a $C_0$-semigroup admits a linear manifold of distributionally irregular vectors. Furthermore, we delve into the study of distributional chaos for the translation $C_0$-semigroup on weighted $L_p$-spaces with a complex sector as the index set. We obtain a sufficient condition for dense distributional chaos, expressed in terms of the weight. In particular, we construct an example of a translation $C_0$-semigroup with a complex sector index set that is Devaney chaotic but not distributionally chaotic.

math.FA↗
arXiv2023

Characterizations of distality via weak equicontinuity

For an infinite discrete group $G$ acting on a compact metric space $X$, we introduce several weak versions of equicontinuity along subsets of $G$ and show that if a minimal system $(X,G)$ admits an invariant measure then $(X,G)$ is distal if and only if it is pairwise IP$^*$-equicontinuous; if the product system $(X\times X,G)$ of a minimal system $(X,G)$ has a dense set of minimal points, then $(X,G)$ is distal if and only if it is pairwise IP$^*$-equicontinuous if and only if it is pairwise central$^*$-equicontinuous; if $(X,G)$ is a minimal system with $G$ being abelian, then $(X,G)$ is a system of order $\infty$ if and only if it is pairwise FIP$^*$-equicontinuous.

math.DS↗
arXiv2022

Broken family sensitivity in transitive systems

Let $(X,T)$ be a topological dynamical system, $n\geq 2$ and $\mathcal{F}$ be a Furstenberg family of subsets of $\mathbb{Z}_+$. $(X,T)$ is called broken $\mathcal{F}$-$n$-sensitive if there exist $δ>0$ and $F\in\mathcal{F}$ such that for every opene (non-empty open) subset $U$ of $X$ and every $l\in\mathbb{N}$, there exist $x_1^l,x_2^l,\dotsc,x_n^l\in U$ and $m_l\in \mathbb{Z}_+$ satisfying $d(T^k x_i^l, T^k x_j^l)> δ,\ \forall 1\leq i 0$. We also obtain specific properties for them by analyzing the factor maps to their maximal equicontinuous factors. Furthermore, we show examples to distinguish different kinds of broken family sensitivity.

math.DS↗
arXiv2022

On $n$-tuplewise IP-sensitivity and thick sensitivity

Let $(X,T)$ be a topological dynamical system and $n\geq 2$. We say that $(X,T)$ is $n$-tuplewise IP-sensitive (resp. $n$-tuplewise thickly sensitive) if there exists a constant $δ>0$ with the property that for each non-empty open subset $U$ of $X$, there exist $x_1,x_2,\dotsc,x_n\in U$ such that \[ \Bigl\{k\in\mathbb{N}\colon \min_{1\le i δ\Bigr\} \] is an IP-set (resp. a thick set). We obtain several sufficient and necessary conditions of a dynamical system to be $n$-tuplewise IP-sensitive or $n$-tuplewise thickly sensitive and show that any non-trivial weakly mixing system is $n$-tuplewise IP-sensitive for all $n\geq 2$, while it is $n$-tuplewise thickly sensitive if and only if it has at least $n$ minimal points. We characterize two kinds of sensitivity by considering some kind of factor maps. We introduce the opposite side of pairwise IP-sensitivity and pairwise thick sensitivity, named (almost) pairwise IP$^*$-equicontinuity and (almost) pairwise syndetic equicontinuity, and obtain dichotomies results for them. In particular, we show that a minimal system is distal if and only if it is pairwise IP$^*$-equicontinuous. We show that every minimal system admits a maximal almost pairwise IP$^*$-equicontinuous factor and admits a maximal pairwise syndetic equicontinuous factor, and characterize them by the factor maps to their maximal distal factors.

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arXiv2020

Some properties of circle maps with zero topological entropy

For a circle map $f\colon\mathbb{S}\to\mathbb{S}$ with zero topological entropy, we show that a non-diagonal pair $\langle x,y\rangle\in \mathbb{S}\times \mathbb{S}$ is non-separable if and only if it is an IN-pair if and only if it is an IT-pair. We also show that if a circle map is topological null then the maximal pattern entropy of every open cover is of polynomial order.

math.DS↗
arXiv2019

Subspaces of interval maps related to the topological entropy

For $a\in [0,+\infty)$, the function space $E_{\geq a}$ ($E_{>a}$; $E_{\leq a}$; $E_{ a}$ are homeomorphic to the Hilbert space $l_2$ and the spaces $E_{\leq a}$ and $E_{<a}$ are contractible. Moreover, the subspaces of $E_{\leq a}$ and $E_{<a}$ consisting of all piecewise monotone maps are homotopy dense in them, respectively.

math.DS↗
arXiv2017

On dynamics of graph maps with zero topological entropy

We explore the dynamics of graph maps with zero topological entropy. It is shown that a continuous map $f$ on a topological graph $G$ has zero topological entropy if and only if it is locally mean equicontinuous, that is the dynamics on each orbit closure is mean equicontinuous. As an application, we show that Sarnak's Möbius Disjointness Conjecture is true for graph maps with zero topological entropy. We also extend several results known in interval dynamics to graph maps. We show that a graph map has zero topological entropy if and only if there is no $3$-scrambled tuple if and only if the proximal relation is an equivalence relation; a graph map has no scrambled pairs if and only if it is null if and only if it is tame.

math.DS↗