论文标题
旋转理论的某些方面关于紧凑型阿贝尔群
Some aspects of Rotation Theory on compact abelian groups
论文作者
论文摘要
在本文中，我们介绍了圆圈的同态同态旋转理论的概括，即一维紧凑型阿贝尔群体，即螺线管群，即{\ it iT}，这些基团将纤维与圆圈纤维纤维与纤维上的cantor abelian组纤维纤维。我们定义旋转元素，\ emph {àla}poincaré，并讨论这些电磁阀基团翻译的动力学特性。当旋转元件产生螺线管基团致密的亚组时，我们还研究了半偶联问题。最后，我们评论这些同态旋转理论与熵之间的关系，因为与圆的情况不同，对于此处考虑的螺线管，这里存在正同态（不是同型身份），具有正熵。
In this paper we present a generalization of Poincaré's Rotation Theory of homeomorphisms of the circle to the case of one-dimensional compact abelian groups which are solenoidal groups, {\it i.e.}, groups which fiber over the circle with fiber a Cantor abelian group. We define rotation elements, \emph{à la} Poincaré and discuss the dynamical properties of translations on these solenoidal groups. We also study the semiconjugation problem when the rotation element generates a dense subgroup of the solenoidal group. Finally, we comment on the relation between Rotation Theory and entropy for these homeomorphisms, since unlike the case of the circle, for the solenoids considered here there are homeomorphisms (not homotopic to the identity) with positive entropy.
