Inducing, slopes, and conjugacy classes

Semiconjugacy to a map of a constant slope

It is well known that a continuous piecewise monotone interval map with positive topological entropy is semiconjugate to a map of a constant slope and the same entropy, and if it is additionally transitive then this semiconjugacy is actually a conjugacy. We generalize this result to piecewise continuous piecewise monotone interval maps, and as a consequence, get it also for piecewise monotone graph maps. We show that assigning to a continuous transitive piecewise monotone map of positive entropy a map of constant slope conjugate to it defines an operator, and show that this operator is not con…

与区间交换映射具有奇异共轭的仿射区间交换变换

Affine IETs with a singular conjugacy to an IET

本研究构造了与标准区间交换映射（IETs）通过奇异共轭拓扑共轭的仿射区间交换变换（AIETs），证明了满足特定斜率与半共轭条件的AIET与对应IET拓扑共轭，且斜率不在稳定空间时共轭为奇异的。

关于仿射区间交换变换的测度与半共轭

On measures and semiconjugacies for affine interval exchange transformations

本文研究双曲周期型仿射区间交换变换的不变测度与共形测度的豪斯多夫维数，给出中心稳定型条件下的精确公式，并推导周期情形下半共轭的最高 Hölder 指数显式公式。