Thermodynamic Formalism for Random Non-uniformly Expanding Maps
Thermodynamic Formalism for Random Non-uniformly Expanding Maps
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DOI：
10.1007/s00220-021-04088-w
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发表时间：
2020-06
影响因子：
2.4
通讯作者：
M. Stadlbauer;Shintaro Suzuki;P. Varandas
中科院分区：
文献类型：
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作者：
M. Stadlbauer;Shintaro Suzuki;P. Varandas
对于一类具有非均匀展开的随机映射，我们提出了一种淬灭的热力学形式，其中不需要马尔可夫结构，不需要一致有界度或存在某些展开动力学。我们证明了每一个可测电位和纤维势在高温下都有一个满足弱吉布斯性质的唯一平衡态，并且相关系数呈指数衰减。这些论点结合了相关性衰减的泛函分析方法（使用Birkhoff锥方法）和carath<s:1> - odory型结构来描述随机动力系统中不必要的紧不变集的相对压力。我们还建立了随机动力系统相对压力的变分原理。
We develop a quenched thermodynamic formalism for a wide class of random maps with non-uniform expansion, where no Markov structure, no uniformly bounded degree or the existence of some expanding dynamics is required. We prove that every measurable and fibered-potential at high temperature admits a unique equilibrium state which satisfies a weak Gibbs property, and has exponential decay of correlations. The arguments combine a functional analytic approach for the decay of correlations (using Birkhoff cone methods) and Carathéodory-type structures to describe the relative pressure of not necessary compact invariant sets in random dynamical systems. We establish also a variational principle for the relative pressure of random dynamical systems.