Several sufficient conditions for sensitive dependence on initial conditions |
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Authors: | Risong Li |
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Affiliation: | a School of Science, Guangdong Ocean University, Zhanjiang, 524025, PR China b Department of Mathematics, Shandong University, Jinan, Shandong 250100, PR China |
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Abstract: | This paper is concerned with sensitive dependence on initial conditions for maps and semi-flows. Several sufficient conditions for sensitive dependence are given, where it is not required that maps and semi-flows are continuous and spaces are compact. In particular, it is shown that if a measure-preserving map (resp. a measure-preserving semi-flow) on a metric probability space with a fully supported measure is topologically strongly ergodic, then it has sensitive dependence. These results relax and extend the conditions of some existing results. |
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Keywords: | 37A05 37A25 54H20 28D05 |
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