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arXiv · 0909.2140

Relative local variational principles for subadditive potentials

Xianfeng Ma·Ercai Chen
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Abstract

We prove two relative local variational principles of topological pressure functions $P(T,\mathcal{F},\mathcal{U},y)$ and$P(T,\mathcal{F},\mathcal{U}|Y)$ for a given factor map $π$, an open cover $\mathcal{U} $ and a subadditive sequence of real-valued continuous functions $\mathcal{F}$. By proving the upper semi-continuity and affinity of the entropy maps $h_{\{\cdot\}}(T,\mathcal{U}\mid Y)$ and $h^+_{\{\cdot\}}(T,\mathcal{U}\mid Y)$ on the space of all invariant Borel probability measures, we show that the relative local pressure $P(T,\mathcal{\{\cdot\}},\mathcal{U}|Y)$ for subadditive potentials determines the local measure-theoretic conditional entropies.

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Xianfeng Ma, Ercai Chen. 2009-09-11. Relative local variational principles for subadditive potentials. https://arxiv.org/abs/0909.2140

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