W-measurable sensitivity of semigroup actions
| Autor: | Bozgan, Francisc, Sanchez, Anthony, Silva, Cesar E., Spielberg, Jack, Stevens, David, Wang, Jane |
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| Rok vydání: | 2018 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | This paper studies the notion of W-measurable sensitivity in the context of semigroup actions. W-measurable sensitivity is a measurable generalization of sensitive dependence on initial conditions. In 2012, Grigoriev et. al. proved a classification result of conservative ergodic dynamical systems that states all are either W-measurably sensitive or act by isometries with respect to some metric and have refined structure. We generalize this result to a class of semigroup actions. Furthermore, a counterexample is provided that shows W-measurable sensitivity is not preserved under factors. We also consider the restriction of W-measurably sensitive semigroup actions to sub-semigroups and show that the restriction remains W-measurably sensitive when the sub-semigroup is large enough (e.g. when the sub-semigroups are syndetic or thick). Comment: 13 pages, 1 Figure. Theorem 5.3 strengthened, typos fixed, some new references added |
| Databáze: | arXiv |
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