Mixing (mathematics)

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

where 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.