平衡态的几何结构
Geometrical constructions of equilibrium states
摘要：
本文报道了在Anosov作用量中含有正则元的一类部分双曲系统--中心等距系统的热力学形式研究的一些进展。该技术是几何风味（特别是，不依赖于符号动力学），甚至提供了新的信息，在经典的情况下。对于这样的系统，我们特别给出了SRB措施和熵最大化措施的存在性的建设性证明。它还建立了非常精细的统计特性（Bernoulliness），并给出了平衡态的表征，在稳定/不稳定的层压，类似于SRB的情况下，他们的条件措施。构造应用于获得的唯一性准不变测度相关联的Hölder雅可比矩阵的horocyclic流。
英文摘要：
In this note we report some advances in the study of thermodynamic formalism for a class of partially hyperbolic system -- center isometries, that includes regular elements in Anosov actions. The techniques are of geometric flavor (in particular, not relying in symbolic dynamics) and even provide new information in the classical case. For such systems, we give in particular a constructive proof of the existence of the SRB measure and of the entropy maximizing measure. It is also established very fine statistical properties (Bernoulliness), and it is given a characterization of equilibrium states in terms of their conditional measures in the stable/unstable lamination, similar to the SRB case. The construction is applied to obtain the uniqueness of quasi-invariant measures associated to Hölder Jacobian for the horocyclic flow.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
