非紧集拓扑压力的热力学定义
A Thermodynamic Definition of Topological Pressure for Non-Compact Sets
摘要：
给出了度量空间的任意（非紧的、非不变的）Borel子集的拓扑压的一个新定义.这个新的量是通过一个合适的变分原理，导致一个平衡态的替代定义。我们研究了这个新量的性质，并将其与现有的拓扑压力概念进行了比较。我们特别感兴趣的情况下，周围的度量空间被假定为紧凑的。我们激励我们的定义的自然性，将其应用到一些有趣的例子，包括水平集的逐点李雅普诺夫指数的Manneville-Pomeau家庭的地图。
英文摘要：
We give a new definition of topological pressure for arbitrary (non-compact, non-invariant) Borel subsets of metric spaces. This new quantity is defined via a suitable variational principle, leading to an alternative definition of an equilibrium state. We study the properties of this new quantity and compare it with existing notions of topological pressure. We are particularly interested in the situation when the ambient metric space is assumed to be compact. We motivate the naturality of our definition by applying it to some interesting examples, including the level sets of the pointwise Lyapunov exponent for the Manneville-Pomeau family of maps.
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