论文标题
关于分段光滑圆同构的不变测度的Hausdorff维度
On the Hausdorff dimension of invariant measures of piecewise smooth circle homeomorphisms
论文作者
论文摘要
我们表明，通常，具有非理性旋转数和零平均非线性（例如，分段线性）的足够规则的分段平滑圆同态同态同态的独特不变度量的量度为零。 为了编码这种通用条件，我们将分段平滑同构视为间隔的通用间隔交换转换（GIET），并依靠组合旋转的概念的吉特（Giets）概念，可以将其视为圆形同型旋转概念的循环概念的扩展，以使圆形旋转概念到Giet设置。
We show that, generically, the unique invariant measure of a sufficiently regular piecewise smooth circle homeomorphism with irrational rotation number and zero mean nonlinearity (e.g., piecewise linear) has zero Hausdorff dimension. To encode this generic condition, we consider piecewise smooth homeomorphisms as generalized interval exchange transformations (GIETs) of the interval and rely on the notion of combinatorial rotation number for GIETs, which can be seen as an extension of the classical notion of rotation number for circle homeomorphisms to the GIET setting.
