科研之友
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摘要
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 X, T x T) is strong scattering @@@ (7) (X x X, T x T) is extremely scattering @@@ (8) For any subset S of a"center dot with upper density 1, there is a c-dense F (sigma) -chaotic set with respect to S. @@@ As an application, the authors show that, for the sub-shift sigma (A) of finite type determined by a k x k-(0, 1) matrix A, sigma (A) is strong mixing if and only if sigma (A) is totally transitive.
