论文标题
除了鲍文的规格属性之外
Beyond Bowen's Specification Property
论文作者
论文摘要
热力学形式主义的经典结果是，对于均匀的双曲系统，每个Hölder连续电势都具有独特的平衡状态。这一事实的一个证明是由于鲁弗斯·鲍恩（Rufus Bowen）所致，并使用了这样的系统满足扩展性和规范属性的事实。在这些注释中，我们调查了使用这些特性的概括将Bowen的论点扩展到统一的双曲线的最新进展，包括对部分双曲线系统的应用和超出负曲率的地理流量的应用。我们包括一个新的标准，用于具有一维中心的部分双曲系统的平衡状态。
A classical result in thermodynamic formalism is that for uniformly hyperbolic systems, every Hölder continuous potential has a unique equilibrium state. One proof of this fact is due to Rufus Bowen and uses the fact that such systems satisfy expansivity and specification properties. In these notes, we survey recent progress that uses generalizations of these properties to extend Bowen's arguments beyond uniform hyperbolicity, including applications to partially hyperbolic systems and geodesic flows beyond negative curvature. We include a new criterion for uniqueness of equilibrium states for partially hyperbolic systems with 1-dimensional center.
