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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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