A characterization of Denjoy flows
A characterization of Denjoy flows
复制标题
Denjoy 流的表征
DOI：
10.1112/blms/24.1.83
复制
发表时间：
1992
影响因子：
0.9
通讯作者：
K. Athanassopoulos
中科院分区：
文献类型：
--
作者：
K. Athanassopoulos
动力系统理论中的一个有趣的问题是从相空间的特征不变子集的性质（如极小集或泊松稳定轨道闭包）确定流的全局结构。对于维数大于2的流形上的流动，在这类集合附近的流动行为还远未被很好地理解。在本说明中，我们给出了一个特征的Denjoy流的环面上，即悬挂的方向保持同胚的单位圆到自己的康托极小集，通过条件指的是渐近行为的轨道附近的严格泊松稳定的轨道封闭。更确切地说，我们证明了以下几点。
An interesting problem in the theory of dynamical systems is to determine the global structure of a flow from properties of characteristic invariant subsets of the phase space such as minimal sets or Poisson stable orbit closures. For flows on manifolds of dimension greater than two, the behaviour of the flow near such sets is far from being well understood. In this note we give a characterization of Denjoy flows on the torus, that is, suspensions of orientation preserving homeomorphisms of the unit circle onto itself with a Cantor minimal set, via conditions referring to the asymptotic behaviour of the orbits near a strictly Poisson stable orbit closure. More precisely, we prove the following.