摘要
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.Under the finiteness and basin conditions,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 gives a clear description of orbit behavior of each point in X except a meager set.
作者
丁义明
孙运
Yiming DING;Yun SUN(Center for Mathematical Sciences,School of Science,Wuhan University of Technology,Wuhan 430070,China)
基金
supported by the National Key Re-search and Development Program of China(2020YFA0714200)
supported by the Excellent Dissertation Cultivation Funds of Wuhan University of Technology(2018-YS-077)。