论文标题
零件光滑的圆形图和某些吉特的刚度
Rigidity for piece-wise smooth circle maps and certain GIETs
论文作者
论文摘要
本文的目的是显示一般间隔交换转换（Giets）的共轭的刚性属性。更确切地说，我们表明，如果两个分段$ c^3 $ giets $ f $和$ g $ g $ a的通用旋转号码具有均值 - 非线性0是同质形态，边界等效性，并且以适当的方式进行了重新构化的方法，那么一组仿射间隔的交换转换，然后将其各自的肾上腺均汇聚为$ conjugating $ c^$ c^1 $ c^$ c^1 $。此外，如果$ f $和$ g $是带有旋转类型组合数据的Giets，通用旋转编号，并且它们是分段圆的差异性，那么它们实际上是$ c^1 $ - 共轭为圆圈的差异性。这些结果概括了K. cunha和D. smania \ cite {cunha_rigity_2014}在分段$ c^3 $ circle Maps的情况下，作者证明对具有旋转类型组合数据组合数据和边界旋转数量的Giets的类似结果。
The goal of this article is to show a rigidity property of conjugacies of generalized interval exchange transformations (GIETs). More precisely, we show that if two piecewise $C^3$ GIETs $f$ and $g$ of generic rotation number with mean-non-linearity 0 are homeomorphic, boundary-equivalent and their renormalizations approach in an appropriate way the set of affine interval exchange transformations, then their respective renormalizations converge to each other and the conjugating map is $C^1$. Moreover, if $f$ and $g$ are GIETs with rotation type combinatorial data, generic rotation number and they are break-equivalent as piecewise circle diffeomorphisms, they are actually $C^1$-conjugated as circle diffeomorphisms. These results generalize the work of K. Cunha and D. Smania \cite{cunha_rigidity_2014} in the case of piecewise $C^3$ circle maps, where the authors prove an analogous result for GIETs with rotation type combinatorial data and bounded rotation number.
