Z^q-作用的定向有界复杂度、平均等度连续与离散谱
动力系统
2022-05-03 v3
摘要
给定 q ∈ N q\in\mathbb{N} q ∈ N ( X , T ) (X,T) ( X , T ) Z q \mathbb{Z}^q Z q v ⃗ ∈ R q ∖ { 0 ⃗ } \vec{v}\in\mathbb{R}^q\setminus\{\vec{0}\} v ∈ R q ∖ { 0 } b ∈ R + q − 1 \textbf{b}\in\mathbb{R}_+^{q-1} b ∈ R + q − 1 ( X , T ) (X,T) ( X , T ) v ⃗ \vec{v} v d k v ⃗ , b d_k^{\vec{v},\textbf{b}} d k v , b d ^ k v ⃗ , b \hat{d}_k^{\vec{v},\textbf{b}} d ^ k v , b d ˉ k v ⃗ , b \bar{d}_k^{\vec{v},\textbf{b}} d ˉ k v , b ( X , T ) (X,T) ( X , T ) { d k v ⃗ , b } k = 1 ∞ \{d_k^{\vec{v},\textbf{b}}\}_{k=1}^{\infty} { d k v , b } k = 1 ∞ { d ^ k v ⃗ , b } k = 1 ∞ \{\hat{d}_k^{\vec{v},\textbf{b}}\}_{k=1}^{\infty} { d ^ k v , b } k = 1 ∞ T T T ( v ⃗ , b ) (\vec{v},\textbf{b}) ( v , b ) ( v ⃗ , b ) (\vec{v},\textbf{b}) ( v , b ) X X X μ \mu μ { d k v ⃗ , b } k = 1 ∞ \{d_k^{\vec{v},\textbf{b}}\}_{k=1}^{\infty} { d k v , b } k = 1 ∞ T T T ( μ , v ⃗ , b ) (\mu,\vec{v},\textbf{b}) ( μ , v , b ) μ \mu μ { d ˉ k v ⃗ , b } k = 1 ∞ \{\bar{d}_k^{\vec{v},\textbf{b}}\}_{k=1}^{\infty} { d ˉ k v , b } k = 1 ∞ μ \mu μ { d ^ k v ⃗ , b } k = 1 ∞ \{\hat{d}_k^{\vec{v},\textbf{b}}\}_{k=1}^{\infty} { d ^ k v , b } k = 1 ∞ T T T ( μ , v ⃗ , b ) (\mu,\vec{v},\textbf{b}) ( μ , v , b ) T T T ( μ , v ⃗ , b ) (\mu,\vec{v},\textbf{b}) ( μ , v , b ) μ \mu μ v ⃗ \vec{v} v
引用
@article{arxiv.2105.03132,
title = {Directional bounded complexity, mean equicontinuity and discrete spectrum for $\mathbb{Z}^q$-actions},
author = {Chunlin Liu and Leiye Xu},
journal= {arXiv preprint arXiv:2105.03132},
year = {2022}
}