Gibbs measures for hyperbolic attractors defined by densities
Gibbs measures for hyperbolic attractors defined by densities
复制标题
由密度定义的双曲吸引子的吉布斯度量
DOI：
10.3934/dcds.2022038
复制
发表时间：
2022
影响因子：
1.1
通讯作者：
M. Pollicott
中科院分区：
文献类型：
--
作者：
D. Parmenter;M. Pollicott
本文将在SRB测度的Sinai、Bowen和Ruelle的基础上，描述双曲吸引子的Gibbs测度的一种新构造。SRB测度的经典构造是基于在一块不稳定流形上推进归一化体积。通过适当地修改每一步的密度，我们表明得到的测度是规定的吉布斯测度。这与Climenhaga-Pesin-Zelerowicz的构造形成了对比，并补充了这一点，后者通过固定的参考度量取代了不稳定流形上的体积。此外，我们的证明的简单性，仅使用不稳定流形和熵估计的增长率的显式性质，具有适用于更一般设置的额外优势。
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.
Anosov 系统某些等距延伸的平衡测度
影响因子：
0.9
作者：
SPATZIER, RALF;VISSCHER, DANIEL
通讯作者：
VISSCHER, DANIEL