This paper introduces generalized ergodicity which contains ergodicity and Lipschitz ergodicity, proves the equivalence relation between generalized ergodicity and chain transitivity and gives its geometrical structure.
For the continuous flows defined on a topological space,we have discussed some properties for the invariant sets and their domains of influence.We have proved the following open problem posed by C.Conley:an attractor ...For the continuous flows defined on a topological space,we have discussed some properties for the invariant sets and their domains of influence.We have proved the following open problem posed by C.Conley:an attractor in a locally connected compact Hausdorff invariant set has finitely many components.In the meantime,two necessary and sufficient conditions for a set to be an attractor have been given.展开更多
基金the National Natural Science Foundation of China (Grant No. 19901034)
文摘This paper introduces generalized ergodicity which contains ergodicity and Lipschitz ergodicity, proves the equivalence relation between generalized ergodicity and chain transitivity and gives its geometrical structure.
基金Phis work was supported by the National Natural Science Foundation of China (Grant No. 19901034) .
文摘For the continuous flows defined on a topological space,we have discussed some properties for the invariant sets and their domains of influence.We have proved the following open problem posed by C.Conley:an attractor in a locally connected compact Hausdorff invariant set has finitely many components.In the meantime,two necessary and sufficient conditions for a set to be an attractor have been given.
