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Several sufficient conditions for a map and a semi-flow to be ergodically sensitive. (English) Zbl 1387.37005
Summary: In this paper, we are concerned solely with the ergodic sensitivity for maps (resp. semi-flows), where these maps and semi-flows may not be continuous (in topology). A few new sufficient conditions under which a map (resp. a semi-flow) on a metric space is ergodically sensitive are presented, where such maps and semi-flows may not be continuous (in topology). In particular, we prove that the topologically strong ergodicity of a measure-preserving map (resp. a measure-preserving semi-flow) on a metric probability space with a fully supported measure implies its ergodical sensitivity.

MSC:
37A05 Dynamical aspects of measure-preserving transformations
37A25 Ergodicity, mixing, rates of mixing
54H20 Topological dynamics (MSC2010)
28D05 Measure-preserving transformations
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