Entropy formulae of conditional entropy in mean metrics. (English) Zbl 1394.37008
Summary: In this paper, we construct the Brin-Katok formula of conditional entropy for invariant measures of continuous maps on a compact metric space by replacing the Bowen metrics with the corresponding mean metrics. Additionally, this paper is also devoted to establishing the Katok’s entropy formula of conditional entropy for ergodic measures in the case of mean metrics.
MSC:
| 37A35 | Entropy and other invariants, isomorphism, classification in ergodic theory |
| 37B05 | Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) |
| 37B20 | Notions of recurrence and recurrent behavior in topological dynamical systems |
| 37A15 | General groups of measure-preserving transformations and dynamical systems |
| 28D20 | Entropy and other invariants |
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