论文标题
广义Veech 1969/Sataev 1975旋转扩展的刚度
Rigidity of generalized Veech 1969/Sataev 1975 extensions of rotations
论文作者
论文摘要
我们查看$ d $ - 点的旋转的旋转$α$带有$ r $标记点的旋转，概括了Veech 1969和Sataev 1975的示例，以及\ cite {fh2}的方形间隔交换转换。我们研究了刚性的刚度，在$α$的ostrowski扩展方面的功能：我们证明，当$α$具有无限的部分代理时，$ t $是刚性的，当与标记点的基本旋转的天然编码是线性的，$ t $并不是刚性的。但是，这两种情况之间仍然存在一个有趣的灰色区域，在这种情况下，我们只在僵化问题上有部分结果。它们使我们能够构建非线性反复和非刚性间隔变换的第一个示例。
We look at $d$-point extensions of a rotation of angle $α$ with $r$ marked points, generalizing the examples of Veech 1969 and Sataev 1975, together with the square-tiled interval exchange transformations of \cite{fh2}. We study the property of rigidity, in function of the Ostrowski expansions of the marked points by $α$: we prove that $T$ is rigid when $α$ has unbounded partial quotients, and that $T$ is not rigid when the natural coding of the underlying rotation with marked points is linearly recurrent. But there remains an interesting grey zone between these two cases, in which we have only partial results on the rigidity question; they allow us to build the first examples of non linearly recurrent and non rigid interval exchange transformations.
