Topological dynamics of transformations induced on the space of probability measures |
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| Authors: | Walter Bauer Karl Sigmund |
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| Institution: | 1. I. Lehrkanzel für Mathematik der Universit?t Salzburg, Porschestra?e 1/I, A-5020, Salzburg, Austria
2. Math. Institut der Universit?t, Strudlhofgasse 4, A-1090, Wien, Austria
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| Abstract: | LetT be a continuous transformation of a compact metric spaceX. T induces in a natural way a transformationT M on the spaceM (X) of probability measures onX, and a transformationT K on the spaceK (X) of closed subsets ofX. This note investigates which of the topological properties ofT∶X→X (like distality, transitivity, mixing property etc. ...) are “inherited” byT M∶M (X)→M (X) andT K∶K (X)→K (X). |
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