论文标题
$ \ mathbb {s}^{1} $的分段上的连续同构绝对连续地图
Continuous homomorphisms on piecewise absolutely continuous maps of $\mathbb{S}^{1}$
论文作者
论文摘要
令$ iet（\ mathbb {s}^{1}）$为$ \ mathbb {s}^{1} $和$ \ Mathcal {ac} _ {+} _ {+} _ {+}（\ mathbb {s}^{1}）$的$ biortion contression contression in in in Inctive intervectiondervistion in in in Incortion。我们用$ \ MATHCAL {ACI} $表示由$ IET（\ Mathbb {s}^{1}）生成的组和$ \ Mathcal {ac} _ {+} _ {+}（\ Mathbb {s s}^{1}}）$。给定$ \ Mathcal {aci} $上的合适距离，我们对所有连续同构$ρ：\ Mathbb {r} \ to \ Mathcal {aci} $进行了分类。更准确地说，$ρ$与连续的同构$ \hatρ：\ mathbb {r} \ to \ mathcal {ac} _ {+}（\ uplus_ {i}（i}）
Let $IET(\mathbb{S}^{1})$ be the group of interval exchange transformation of $\mathbb{S}^{1}$ and $\mathcal{AC}_{+}(\mathbb{S}^{1})$ be the group of absolutely continuous preserving orientation bijection with inverse absolutely continuous. We denote by $\mathcal{ACI}$ the group generated by $IET(\mathbb{S}^{1})$ and $\mathcal{AC}_{+}(\mathbb{S}^{1})$. Given a suitable distance on $\mathcal{ACI}$, we classify all continuous homomorphisms $ρ:\mathbb{R} \to \mathcal{ACI}$. More precisely, $ρ$ is conjugated to a continuous homomorphism $\hatρ:\mathbb{R} \to \mathcal{AC}_{+}(\uplus_{i}(\mathbb{S}^{1})_{i})$.
