(Un)distorted diffeomorphisms in different regularities

Some examples of distorted interval diffeomorphisms of intermediate regularity

We improve a recent construction of Andrés Navas to produce the first examples of $C^2$-undistorted diffeomorphisms of the interval that are $C^{1+α}$-distorted (for every $α< 1$). We do this via explicit computations due to the failure of an extension to class $C^{1+α}$ of a classical lemma related to the work of Nancy Kopell.

如何（不）证明一维流形上微分同胚的（非）扭曲性

How (not) to prove (un)distortion for diffeomorphisms of one-manifolds

研究给定一维流形\(M\)及\(1\leq r\lt s\leq\infty\)，是否存在\(C^s\)保向紧支微分同胚在\(\mathrm{Diff}_{c,+}^s(M)\)中无扭曲但在更大的\(C^r\)微分同胚群中有扭曲。分析了不同\((r,s)\)情况及相关阻碍。

一维流形微分同胚的几乎可约性、畸变与局部完美性

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

本文证明圆周和实直线紧支撑光滑微分同胚群中元素畸变当且仅当几乎可约，并借助新的局部完美性结果建立该等价性。

光滑流形的初等等价与微分同胚群

Elementary equivalence and diffeomorphism groups of smooth manifolds

该研究证明了光滑流形的微分同胚群在初等等价下必然同胚，且在二维及以上维度中，保持光滑体积形式的微分同胚群也具有类似性质。

Distortion and Tits alternative in smooth mapping class groups

In this article, we study the smooth mapping class group of a surface S relative to a given Cantor set, that is the group of isotopy classes of orientation-preserving smooth diffeomorphisms of S which preserve this Cantor set. When the Cantor set is the standard ternary Cantor set, we prove that the subgroup consisting of diffeomorphisms which are isotopic to the identity on S does not contain any distorted elements. Moreover, we prove a weak Tits alternative for these groups.