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arXiv · 1102.3846

A local variational principle for random bundle transformations

Xianfeng Ma·Ercai Chen
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Abstract

We introduce local topological entropy $h_{\text{top}}(T, \mathcal{U})$ and two kinds of local measure-theoretic entropy $h_{\mu}^{(r)-}(T,\mathcal{U})$ and $h_{\mu}^{(r)+}(T,\mathcal{U})$ for random bundle transformations. We derive a variational inequality of random local entropy for $h_{\mu}^{(r)+}(T,\mathcal{U})$. As an application of such relation we prove a local variational principle in random dynamical system.

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Xianfeng Ma, Ercai Chen. 2011-02-18. A local variational principle for random bundle transformations. https://arxiv.org/abs/1102.3846

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