论文标题
热力学形式主义，用于随机非均匀扩展地图
Thermodynamic formalism for random non-uniformly expanding maps
论文作者
论文摘要
我们为具有不均匀扩展的广泛的随机地图开发了淬火的热力学形式主义，其中不需要马尔可夫结构，不统一界限或存在一些扩展的动力学。我们证明，在高温下，每个可测量和光纤$ c^1 $ - 电位都可以满足弱Gibbs属性的独特平衡状态，并且具有指数性的相关性衰减。该参数结合了一种功能分析方法，以衰减相关性（使用Birkhoff锥方法）和Carathéodory-type结构，以描述随机动力学系统中不需必要的紧凑型不变集的相对压力。我们还建立了随机动力学系统相对压力的变异原理。
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 $C^1$-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.
