论文标题
SRB和平衡度量通过维度理论
SRB and equilibrium measures via dimension theory
论文作者
论文摘要
众所周知，统一双曲线流的SRB和平衡度量在稳定和不稳定的叶子的措施方面接受了产品结构，并具有由潜在功能给出的缩放特性。我们描述了类似于豪斯多夫度量的定义的这些叶子测量的结构，依靠佩辛 - 孔塞克尔对拓扑压力的描述为使用鲍恩球作为维度特征。作者YA为离散时间系统构建了这些叶子测量。 Pesin和A. Zelerowicz。在此处的连续时间设置中，对缩放属性的描述更加完整，我们使用具有双面Bowen球的类似过程来直接产生平衡度量本身。
It is well-known that SRB and equilibrium measures for uniformly hyperbolic flows admit a product structure in terms of measures on stable and unstable leaves with scaling properties given by the potential function. We describe a construction of these leaf measures analogous to the definition of Hausdorff measure, relying on the Pesin-Pitskel' description of topological pressure as a dimensional characteristic using Bowen balls. These leaf measures were constructed for discrete-time systems by the author, Ya. Pesin, and A. Zelerowicz. In the continuous-time setting here, the description of the scaling properties is more complete, and we use a similar procedure with two-sided Bowen balls to directly produce the equilibrium measure itself.
