论文标题
一维洛伦兹样扩展地图的相变
Phase Transitions for one-dimensional Lorenz-like expanding Maps
论文作者
论文摘要
给定一维洛伦兹的扩展地图，我们证明条件\ linebreak $ p_ {top}（ϕ，ϕ，\ partial \ mathcal {p}，\ ell）<p_ {top}（top}（top}（ϕ，\ ell）$ $ ϕ：[0,1] \ longrightArrow \ Mathbb {r} $。我们将其应用于证明准霍德连续电位（有关定义，请参见第2.2小节）最多具有一个平衡度量，我们构建了一个连续但不是Hölder的家族，也不是弱的Hölder连续潜力，我们观察到相位过渡。实际上，该类包括所有霍尔德和弱 - 霍尔德的连续潜力，并形成开放式和[2]。
Given an one-dimensional Lorenz-like expanding map we prove that the condition\linebreak $P_{top}(ϕ,\partial \mathcal{P},\ell)<P_{top}(ϕ,\ell)$ (see, subsection 2.4 for definition), introduced by Buzzi and Sarig in [1] is satisfied for all continuous potentials $ϕ:[0,1]\longrightarrow \mathbb{R}$. We apply this to prove that quasi-Hölder-continuous potentials (see, subsection 2.2 for definition) have at most one equilibrium measure and we construct a family of continuous but not Hölder and neither weak Hölder continuous potentials for which we observe phase transitions. Indeed, this class includes all Hölder and weak-Hölder continuous potentials and form an open and [2].
