Pre-image variational principle for bundle random dynamical systems
Xianfeng Ma Ercai Chen
Discrete & Continuous Dynamical Systems - A 2009, 23(3): 957-972 doi: 10.3934/dcds.2009.23.957
The pre-image topological pressure is defined for bundle random dynamical systems. A variational principle for it has also been given.
keywords: Pre-image topological pressure Random dynamical systems Variational principle
Entropy formulae of conditional entropy in mean metrics
Ping Huang Ercai Chen Chenwei Wang
Discrete & Continuous Dynamical Systems - A 2018, 38(10): 5129-5144 doi: 10.3934/dcds.2018226

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.

keywords: Conditional entropy Brin-Katok formula Katok' entropy formula mean metrics measure decomposition

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