On Bowen’s entropy inequality and almost specification for flows. (English) Zbl 1506.37022
The authors extend the definition of topological entropy to flows on non-compact sets in a way that it coincides with the Bowen topological entropy of time-1 maps. In this framework an Abramov-type formula is proven and the authors obtain an equivalent of the Bowen inequality.
Saturated flows are investigated and a condition is obtained (expressed in terms of the time-\(t\) map of the flow) that implies saturation of the flow.
Next, an almost specification property is defined for flows and it is equivalent to the (discrete) almost specification property for time-1 maps. It is also shown that every continuous flow with the almost specification property is saturated.
Reviewer: Marcin Kulczycki (Kraków)
MSC:
| 37B40 | Topological entropy |
| 37A35 | Entropy and other invariants, isomorphism, classification in ergodic theory |
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