论文标题
一个拓扑吸引子
α-limit sets and Lyapunov function for maps with one topological attractor
论文作者
论文摘要
我们考虑了连续地图的拓扑行为，其中一个拓扑吸引子在紧凑的度量空间$ x $上。这种图是对图的概括，例如拓扑膨胀的洛伦兹地图，没有homtervals的单峰地图等。我们为此类地图提供了级别的$ a $ r $ $ $对分解，并表征每个点的$α$ limit集。基于$ x $的弱摩尔斯分解，我们构建了一个有界的lyapunov函数$ v（x）$，除了微薄的集合外，$ x $中每个点的轨道行为清晰描述。
We consider the topological behaviors of continuous maps with one topological attractor on compact metric space $X$. This kind of map is a generalization of maps such as topologically expansive Lorenz map, unimodal map without homtervals and so on. We provide a leveled $A$-$R$ pair decomposition for such maps, and characterize $α$-limit set of each point. Based on weak Morse decomposition of $X$, we construct a bounded Lyapunov function $V(x)$, which give a clear description of orbit behavior of each point in $X$ except a meager set.
