On special flows over IETs that are not isomorphic to their inverses

某些区间交换变换的初等可容许子群

Some elementary amenable subgroups of interval exchange transformations

本文研究了区间交换变换中某些初等可容许子群的性质，探讨了其非虚拟可解性和可解性条件，并展示了无限多个非线性且非虚拟可解的群以及可解群的导出长度。

Interval exchanges that do not embed in free groups

A disjoint rotation map is an interval exchange transformation (IET) on the unit interval that acts by rotation on a finite number of invariant subintervals. It is currently unknown whether the group E of all IETs possesses any non-abelian free subgroups. It is shown that it is not possible for a disjoint rotation map to occur in a subgroup of E that is isomorphic to a non-abelian free group.

generalized区间交换变换与其逆变换在冻结时正则性之间的意外差异

A surprising discrepancy in the regularity of conjugacies between generalized interval exchange transformations and their inverses at freezing

研究揭示了广义区间交换变换与其逆在冻结时正则性的不对称行为，通过热力学正则化和零温极限分析，获得Hausdorff维度和Hölder指数的渐进行为。

The inverse problem for canonically bounded rank-one transformations

Given the cutting and spacer parameters for a rank-1 transformation, there is a simple condition which is easily seen to be sufficient to guarantee that the transformation under consideration is isomorphic to its inverse. Here we show that if the cutting and spacer parameters are canonically bounded, that condition is also necessary, thus giving a simple characterization of the canonically bounded rank-1 transformations that are isomorphic to their inverse.

非对称混合泊松悬吊

Asymmetric mixing Poisson suspensions

研究发现某些混合泊松悬吊不与其逆运算同构，揭示了非对称混合过程的特性。

On typicality of translation flows which are disjoint with their inverse

In this paper we prove that translation structures for which the corresponding vertical translation flows is weakly mixing and disjoint with its inverse, form a $G_δ$-dense set in every non-hyperelliptic connected component of the moduli space $\mathcal M$. This is in contrast to hyperelliptic case, where for every translation structure the associated vertical flow is isomorphic to its inverse. To prove the main result, we study limits of the off-diagonal 3-joinings of special representations of vertical translation flows. Moreover, we construct a locally defined continuous embedding of the mo…