In this work, by virtue of the properties of weakly almost periodic points of a dynamical system （X, T） with at least two points, the authors prove that, if the measure center M（T） of T is the whole space, that is...In this work, by virtue of the properties of weakly almost periodic points of a dynamical system （X, T） with at least two points, the authors prove that, if the measure center M（T） of T is the whole space, that is, M（T） = X, then the following statements are equivalent： （1） （X, T） is ergodic mixing; （2） （X, T） is topologically double ergodic; （3） （X, T） is weak mixing; （4） （X, T） is extremely scattering; （5） （X, T） is strong scattering; （6） （X × X, T × T） is strong scattering; （7） （X × X, T × T） is extremely scattering; （8） For any subset S of N with upper density 1, there is a c-dense Fα-chaotic set with respect to S. As an application, the authors show that, for the sub-shift aA of finite type determined by a k × k-（0, 1） matrix A, erA is strong mixing if and only if aA is totally transitive.展开更多
基金supported by the National Natural Science Foundation of China (No. 10971236)the Foundation of Jiangxi Provincial Education Department (No. GJJ11295)the Jiangxi Provincial Natural Science Foundation of China (No. 20114BAB201006)
文摘In this work, by virtue of the properties of weakly almost periodic points of a dynamical system （X, T） with at least two points, the authors prove that, if the measure center M（T） of T is the whole space, that is, M（T） = X, then the following statements are equivalent： （1） （X, T） is ergodic mixing; （2） （X, T） is topologically double ergodic; （3） （X, T） is weak mixing; （4） （X, T） is extremely scattering; （5） （X, T） is strong scattering; （6） （X × X, T × T） is strong scattering; （7） （X × X, T × T） is extremely scattering; （8） For any subset S of N with upper density 1, there is a c-dense Fα-chaotic set with respect to S. As an application, the authors show that, for the sub-shift aA of finite type determined by a k × k-（0, 1） matrix A, erA is strong mixing if and only if aA is totally transitive.
