论文标题
由密度定义的双曲线吸引子的吉布斯度量
Gibbs measures for hyperbolic attractors defined by densities
论文作者
论文摘要
在本文中，我们将描述一种新的吉布斯措施，用于夸张的吸引者，概括了西奈，鲍恩和SRB措施的原始结构。 SRB度量的经典结构是基于推动不稳定歧管上的归一化体积。通过适当地修改每个步骤的密度，我们表明所得的度量是规定的吉布斯度量。这与Climenhaga-pesin-Zelerowicz的构建形成鲜明对比，并补充了，后者用固定的参考度量代替了不稳定歧管上的体积。此外，我们的证明的简单性仅在不稳定的多种流形和熵估计的增长率上使用明确的属性，具有在更一般的设置中适用的附加优势。
In this article we will describe a new construction for Gibbs measures for hyperbolic attractors generalizing the original construction of Sinai, Bowen and Ruelle of SRB measures. The classical construction of the SRB measure is based on pushing forward the normalized volume on a piece of unstable manifold. By modifying the density at each step appropriately we show that the resulting measure is a prescribed Gibbs measure. This contrasts with, and complements, the construction of Climenhaga-Pesin-Zelerowicz who replace the volume on the unstable manifold by a fixed reference measure. Moreover, the simplicity of our proof, which uses only explicit properties on the growth rate of unstable manifold and entropy estimates, has the additional advantage that it applies in more general settings.
