环面耦合Anosov同态格的SRB测度的解析性
Analyticity of the SRB measure of a lattice of coupled Anosov diffeomorphisms of the torus
摘要：
我们考虑的“热力学极限”的d维格子的双曲动力系统的2-环面，通过弱和最近邻耦合相互作用。我们证明了SRB测度在耦合强度上是解析的。证明是基于符号动力学技术，使我们能够映射到一个（d+1）维晶格上的自旋系统的吉布斯措施的SRB措施。这个吉布斯测度可以通过通常的“簇扩展”技术的扩展（抽取）来研究。
英文摘要：
We consider the "thermodynamic limit"of a d-dimensional lattice of hyperbolic dynamical systems on the 2-torus, interacting via weak and nearest neighbor coupling. We prove that the SRB measure is analytic in the strength of the coupling. The proof is based on symbolic dynamics techniques that allow us to map the SRB measure into a Gibbs measure for a spin system on a (d+1)-dimensional lattice. This Gibbs measure can be studied by an extension (decimation) of the usual "cluster expansion" techniques.
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