论文标题
随机压力函数的变分原理
Variational principle of random pressure function
论文作者
论文摘要
本文旨在为随机动力学系统的随机压力函数开发一种凸分析方法。使用一些凸分析技术和功能分析，我们建立了一个随机压力函数的变异原理，该原理扩展了BIS等。工作（对熵功能，变异原理和平衡状态的凸分析方法，Comm。Math。Phys。（2022）\ TextBf {394} 215-256）和Ruelle的工作（统计机制（统计机制）设置为$ \ MATHBB {Z}^Z}^v n维n $ Action Action Asperificate and Specification and Specialitive and Secification，Trans coodification，trans。 \ textbf {187} 237-251）到随机动力学系统。 本文提供了一种策略，以获取一些适当的变异原理，以涉及熵样数量的动力学系统，以将拓扑动态和千差论理论联系起来。作为应用，我们建立了$ \ mathbb {z} $的零熵系统的最大图案熵和多项式拓扑熵的变异原理 - 动作，动作，无限熵系统的平均尺寸，由正常的熵组和不可转换的随机动态系统的前图熵量和类似于前图的熵量。
This paper aims to develop a convex analysis approach to random pressure functions of random dynamical systems. Using some convex analysis techniques and functional analysis, we establish a variational principle for random pressure function, which extends Bis et al. work (A convex analysis approach to entropy functions, variational principles and equilibrium states, Comm. Math. Phys. (2022) \textbf{394} 215-256) and Ruelle's work (Statistical mechanics on a compact set with $\mathbb{Z}^ν$ action satisfying expansiveness and specification, Trans. Amer. Math. Soc. (1973) \textbf{187} 237-251) to random dynamical systems. The present paper provides a strategy of obtaining some proper variational principles for entropy-like quantities of dynamical systems to link the topological dynamics and ergodic theory. As applications, we establish variational principles of maximal pattern entropy and polynomial topological entropy of zero entropy systems of $\mathbb{Z}$-actions, mean dimensions of infinite entropy systems acting by amenable groups and preimage entropy-like quantities of non-convertible random dynamical systems.
