论文标题
LELEK粉丝的瞬时同构
A transitive homeomorphism on the Lelek fan
论文作者
论文摘要
令$ x $为连续体，让$φ：x \ rightarrow x $为同构。要构建具有有趣的动力学属性的动态系统$（x，φ）$，Continuum $ x $通常需要具有一些复杂的拓扑结构。在本文中，我们对这种动态属性感兴趣：传递性。到现在为止，已经构建了Continua $ x $的各种示例，以使动力学系统$（x，φ）$具有传递性。通常，它们是连续的示例，这些示例未与路径连接，例如伪弧或伪圆，或者它们是本地连接的continua的示例（并且每个本地连接的连续体都是路径连接的），Wazewski的Universal Dendrite and Sierpinski and Sierpinski and Sierpinski Carpets exultem carpetsements。 在本文中，我们介绍了动态系统$（x，φ）$的示例，其中$φ$是连续$ x $和$ x $的同态性的同态性，是与路径连接但不是本地连接的连续体。我们在LELEK粉丝上构建了瞬态同态。作为副产品，还构建了LELEK风扇上的不可转化的及时图。
Let $X$ be a continuum and let $φ:X\rightarrow X$ be a homeomorphism. To construct a dynamical system $(X,φ)$ with interesting dynamical properties, the continuum $X$ often needs to have some complicated topological structure. In this paper, we are interested in one such dynamical property: transitivity. By now, various examples of continua $X$ have been constructed in such a way that the dynamical system $(X,φ)$ is transitive. Mostly, they are examples of continua that are not path-connected, such as the pseudo-arc or the pseudo-circle, or they are examples of locally connected continua (and every locally connected continuum is path-connected), Wazewski's universal dendrite and the Sierpinski carpet are such examples. In this paper, we present an example of a dynamical system $(X,φ)$, where $φ$ is a homeomorphism on the continuum $X$ and $X$ is a path-connected but not locally connected continuum. We construct a transitive homeomorphism on the Lelek fan. As a by-product, a non-invertible transitive map on the Lelek fan is also constructed.
