Several sufficient conditions for a map and a semi-flow to be ergodically sensitive

摘要

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.