论文标题
洛伦兹吸引子在任何维度上的平衡状态的独特性
Uniqueness of equilibrium states for Lorenz attractors in any dimension
论文作者
论文摘要
在本说明中，我们考虑了洛伦兹在任何维度上吸引洛伦兹吸引者的热力学形式主义。在Hölder连续电势函数$ ϕ $的温和条件下，我们证明，对于$ C^1 $向量场的开放和密集的子集，每个Lorenz吸引子都支持独特的平衡状态。特别是，我们获得了量度最大熵的唯一性。
In this note, we consider the thermodynamic formalism for Lorenz attractors of flows in any dimension. Under a mild condition on the Hölder continuous potential function $ϕ$, we prove that for an open and dense subset of $C^1$ vector fields, every Lorenz attractor supports a unique equilibrium state. In particular, we obtain the uniqueness for the measure of maximal entropy.
