论文标题
关于完整的自由式亚伯时代自由小组的延伸动力学的动态
On the dynamics of extensions of free-abelian times free groups endomorphisms to the completion
论文作者
论文摘要
我们获得了均匀的连续性条件，用于通过将每个组件中的前缀度量指标定义的自由式时代自由时代的内态性，并确定该度量的均匀连续性与保留粗大的Median之间的等价性，该指标最近是由Fioravanti引入的。考虑到内态的扩展到完成，我们计算了在无限固定点（分别定期）点集的固定点（分别定期）点子组（分别定期）点的作用的轨道数。最后，我们研究了无限点的动力学：对于某些内态性，以精确的方式定义，适合Delgado和Ventura给出的分类，我们证明每个无限点都是周期性或徘徊，这意味着动态是渐变的。我们还证明了后者的自动形态案例。
We obtain conditions of uniform continuity for endomorphisms of free-abelian times free groups for the product metric defined by taking the prefix metric in each component and establish an equivalence between uniform continuity for this metric and the preservation of a coarse-median, which was recently introduced by Fioravanti. Considering the extension of an endomorphism to the completion we count the number of orbits for the action of the subgroup of fixed points (resp. periodic) points on the set of infinite fixed (resp. periodic) points. Finally, we study the dynamics of infinite points: for some endomorphisms, defined in a precise way, fitting a classification given by Delgado and Ventura, we prove that every infinite point is either periodic or wandering, which implies that the dynamics is asymptotically periodic. We also prove the latter for the case of automorphisms.
