On the Dynamics of Translated Cone Exchange Transformations

尽管数值实验(见Ashwin P.，Goetz A.，Peres P.，Rodrigues A.，(2018).区间交换变换到平面分段等距中的嵌入，遍历理论和动力系统，1-27)，支持集合${\mathcal U(\lambda，\eta)$对于所考虑的参数应该是非空的，不知道这是否是真的。事实上，这与这一研究领域最大的悬而未决的问题之一有关：PWI的典型家庭是否支持嵌入IET。

Although numerical experiments (see Ashwin P., Goetz A., Peres P., Rodrigues A., (2018). Embeddings of Interval Exchange Trans-formations into Planar Piecewise Isometries, Ergodic Theory and Dynamical Systems, 1-27), support that the set ${\mathcal U(\lambda, \eta)$ should be nonempty for the parameters in consideration, it is not known whether this is true. Indeed, thisis related to one of the greatest open questions in this field of study: whether typical families of PWIs support embeddings of IETs.