标题： 几乎可约性、扭曲性和一维流形微分同胚的局部完美性 显示英文标题

标题： Almost reducibility, distortion and local perfection for diffeomorphisms of one-manifolds

摘要： 在本文中，我们表征了圆的光滑微分同胚群和实直线上的紧支撑光滑微分同胚群的畸变元素。 更准确地说，我们证明，在这种情况下，一个元素是畸变的当且仅当它是几乎可约的，即当且仅当它有共轭任意接近于等距变换。 对于具有固定点的微分同胚，我们证明这等价于它是没有双曲零点的C1向量场的时间-1映射。 畸变与几乎可约性之间的等价性依赖于关于流形微分同胚群中畸变元素的新更一般的结果，以及关于实直线上紧支撑光滑微分同胚群的新局部完美结果。 显示英文摘要

摘要： In this article, we characterize the distortion elements of the group of smooth diffeomorphisms of the circle and of the group of compactly supported smooth diffeomorphisms of the real line. More precisely, we prove that, in this context, an element is distorted if and only if it is almost reducible, that is if and only if it has conjugates arbitrarily close to an isometry. For diffeomorphisms with fixed points, we show that this is equivalent to being the time-1 map of a C 1 vector field without hyperbolic zero. The equivalence between distortion and almost reducibility relies on new more general results about distortion elements in groups of diffeomorphisms of manifolds and on a new local perfection result for the group of compactly supported smooth diffeomorphisms of the real line.