Null flows and null functions on \(\mathbb R\). (English) Zbl 1092.37005
Summary: We introduce the notion of null flows via sequence entropy. We study the structure of minimal null flows and show that such a flow is almost automorphic and uniquely ergodic. Moreover, minimal null functions on \(\mathbb R\) are defined and investigated. At the same time, we show that the set of almost automorphic flows strictly contains the set of minimal null flows which strictly contains the set of almost-periodic flows.
MSC:
| 37A35 | Entropy and other invariants, isomorphism, classification in ergodic theory |
| 37B40 | Topological entropy |
| 37B05 | Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) |
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