论文标题
Geller和Misiurewicz关于粗糙结合的两个猜想
Two conjectures on coarse conjugacy by Geller and Misiurewicz
论文作者
论文摘要
在对粗熵的研究中，W。Geller和M. Misiurewicz引入了粗共轭的概念：一种适合于从远处观察到的度量空间动力学的共轭性版本。他们对粗略的共轭性做出了两个猜想，从而推广了他们的结果。我们反驳了这两个猜想。我们研究了额外假设对猜想有效性的影响：我们表明，Geller和Misiurewicz对其中一个猜想的结果可以认为是最佳的，并且我们证明了在参考工作中互补的假设下的另一个猜想。
In their study of coarse entropy, W. Geller and M. Misiurewicz introduced the notion of coarse conjugacy: a version of conjugacy appropriate for dynamics on metric spaces observed from afar. They made two conjectures on coarse conjugacy generalising their results. We disprove both of these conjectures. We investigate the impact of extra assumptions on the validity of the conjectures: We show that the result of Geller and Misiurewicz towards one of the conjectures can be considered optimal, and we prove the other conjecture under an assumption complementary to that from the referenced work.
