Mixing (mathematics)

（重定向自Topological transitivity）

A form of mixing may be defined without appeal to a measure, only using the topology of the system. A continuous map $f:X\to X$ is said to be topologically transitive if, for every pair of non-empty open sets $A,B\subset X$ , there exists an integer n such that

where $f^n$ is the nth iterate of f. In the operator theory, a topologically transitive bounded linear operator (a continuous linear map on a topological vector space) is usually called hypercyclic operator. A related idea is expressed by the wandering set.

单词	Topological transitivity
释义	Topological transitivity 英语百科 Mixing (mathematics) （重定向自Topological transitivity） A form of mixing may be defined without appeal to a measure, only using the topology of the system. A continuous map $f:X\to X$ is said to be topologically transitive if, for every pair of non-empty open sets $A,B\subset X$ , there exists an integer n such that where $f^n$ is the nth iterate of f. In the operator theory, a topologically transitive bounded linear operator (a continuous linear map on a topological vector space) is usually called hypercyclic operator. A related idea is expressed by the wandering set.
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