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Change of velocity and ergodicity in flows and in Markov semi-groups

1977; Springer Nature; Volume: 39; Issue: 3 Linguagem: Inglês

10.1007/bf00535472

0044-3719

Michael Lin, John T. Montgomery, Robert Sine,

Advanced Operator Algebra Research

Let {T(t)}t≧0 be a strongly continuous semi-group of Markov operators on C(X) with generator G. If m∃C(X) is strictly positive, mG generates a semigroup. If {T(t)} is a group given by a flow, m may have isolated zeros and, under some regularity conditions, mG will still generate a flow, constructed explicitly. The connection between some ergodic properties of the new and original flow is studied. For the Markov semi-groups, the new one is strongly ergodic if and only if the original one is strongly ergodic.