论文标题
通过密度为某些部分双曲线吸引子构建平衡状态
Constructing equilibrium states for some partially hyperbolic attractors via densities
论文作者
论文摘要
我们将描述一类部分双曲系统的新结构。这概括了我们在均匀双曲机环境中进行吉布斯度量的构建。这种更通用的设置引入了我们需要仔细解决的新问题，特别是需要对转换的其他假设。我们处理两种情况：中心稳定的歧管满足有限的膨胀条件；或中心不稳定的歧管满足了一个次指数收缩条件，在平衡状态构建体的背景下似乎是新的。以前，佩辛·西奈（Pesin-Sinai）和多尔戈波（Dolgopyat）在特定的U-GIBBS测量情况下，以及Climenhaga，Pesin和selerowicz构建平衡状态的问题。
We shall describe a new construction of equilibrium states for a class of partially hyperbolic systems. This generalises our construction for Gibbs measures in the uniformly hyperbolic setting. This more general setting introduces new issues that we need to address carefully, in particular requiring additional assumptions on the transformation. We treat two cases: either the centre-stable manifold satisfies a bounded expansion condition; or the centre-unstable manifold satisfies a subexponential contraction condition which appears new in the context of equilibrium state constructions. The problem of constructing equilibrium states was previously raised by Pesin-Sinai and Dolgopyat for the particular case of u-Gibbs measures, and by Climenhaga, Pesin and Zelerowicz for other equilibrium states.
