Conditional Entropy Formula with Respect to Monotonic Partitions
Journal of Dynamical and Control Systems(2024)
摘要
We investigate conditional entropy with respect to monotonic (invariant, decreasing, or increasing) measurable partitions. In particular, we obtain Brin-Katok’s and Katok’s entropy formula for conditional entropy with respect to invariant, decreasing and a large class of increasing partitions. Our proofs develop new adaptions on applying conditional variants of Shannon-McMillan-Breiman theorems corresponding to the monotonic partitions, to link with the local and global conditional entropy forms. As an application, we obtain a number of reformulations of the unstable entropy for ergodic measures of general C^r(r>1) diffeomorphisms.
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关键词
Brin-Katok formula,Katok’s formula,Measure decomposition,Conditional entropies,Primary: 37A35,28A50,28D20
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