Westudytheconditional entropy of topological dynamical systems using a family of metrics induced by probability bi-sequences. We present a Brin-Katok formula by replacing the mean metric by a family of metrics induced by a probability bi-sequence. We also establish the Katoks entropy formula for conditional entropy for ergodic measures in the case of the new family of metrics.
M. RAHIMI
,
N. BIDABADI
. A FORMULA OF CONDITIONAL ENTROPY FOR METRICS INDUCED BY PROBABILITY BI-SEQUENCES[J]. Acta mathematica scientia, Series B, 2025
, 45(4)
: 1619
-1639
.
DOI: 10.1007/s10473-025-0420-3
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