论文标题
非均匀光谱的动力学方法
A dynamical approach to nonhomogeneous spectra
论文作者
论文摘要
令$α> 0 $和$ 0 <γ<1 $。定义$ g_ {α，γ} \ colon \ mathbb {n} \ to \ mathbb {n} _0 $ by $ g_ {α，γ}（n）= \ lfloornα+γ\γ\ rfloor $集合$ g_ {α，γ}（\ mathbb {n}）= \ {g_ {α，γ}（n）\ colon n \ in \ mathbb {n} \} $称为$γ$ - nonhonhososos speptrum $ $ $α$。通过扩展，函数$ g_ {α，γ} $称为光谱。 1996年，伯格森（Bergelson），辛德曼（Hindman）和KRA表明，功能$ g_ {α，γ} $保留了$ \ mathbb {n} $的子集的一定程度，也就是说，如果子集$ a $ a $ a $ a $ \ a $ \ mathbb {n} $是ip-set，ip set，一套$ $^$^*$^*$^*$^*$^*$^*$^*$^*$^*$ - $ g_ {α，γ}（a）$是所有$α> 0 $和$ 0 <γ<1 $的相应对象。 2012年，Hindman和Johnson扩展了这一结果，其中包括其他几个宽敞的概念：C-set，J-set，强烈的中央集合和分段联合套件。我们在此问题上采用了动态方法，并在光谱的保存和悬架的升力属性之间建立了对应关系。作为应用程序，我们给出了一些已知结果的统一证明，并获得了一些新的结果。
Let $α>0$ and $0<γ<1$. Define $g_{α,γ}\colon \mathbb{N}\to\mathbb{N}_0$ by $g_{α,γ}(n)=\lfloor nα+γ\rfloor$, where $\lfloor x \rfloor$ is the largest integer less than or equal to $x$. The set $g_{α,γ}(\mathbb{N})=\{g_{α,γ}(n)\colon n\in\mathbb{N}\}$ is called the $γ$-nonhomogeneous spectrum of $α$. By extension, the functions $g_{α,γ}$ are referred to as spectra. In 1996, Bergelson, Hindman and Kra showed that the functions $g_{α,γ}$ preserve some largeness of subsets of $\mathbb{N}$, that is, if a subset $A$ of $\mathbb{N}$ is an IP-set, a central set, an IP$^*$-set, or a central$^*$-set, then $g_{α,γ}(A)$ is the corresponding object for all $α>0$ and $0<γ<1$. In 2012, Hindman and Johnson extended this result to include several other notions of largeness: C-sets, J-sets, strongly central sets, and piecewise syndetic sets. We adopt a dynamical approach to this issue and build a correspondence between the preservation of spectra and the lift property of suspension. As an application, we give a unified proof of some known results and also obtain some new results.
