Sensitive Dependence of Geometric Gibbs States at Positive Temperature
Sensitive Dependence of Geometric Gibbs States at Positive Temperature
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DOI：
10.1007/s00220-019-03350-6
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发表时间：
2018-04
影响因子：
2.4
通讯作者：
D. Coronel;Juan Rivera-Letelier
中科院分区：
文献类型：
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作者：
D. Coronel;Juan Rivera-Letelier
我们给出了第一个例子的光滑家庭的真实的和复杂的地图具有敏感的依赖性的几何吉布斯状态在正温度。这个族由在强意义上非一致双曲的类二次映射组成。我们表明，在家庭中的一个密集的映射集的几何吉布斯状态不收敛于正温度。这是统计力学或热力学形式主义在正温度下不收敛的第一个例子，并回答了货车Enter和Russel的一个问题。我们还表明，这种现象是强大的：有一个开放的分析2-参数家庭的二次类映射，表现出敏感的几何吉布斯状态在正温度的依赖。
We give the first example of a smooth family of real and complex maps having sensitive dependence of geometric Gibbs states at positive temperature. This family consists of quadratic-like maps that are non-uniformly hyperbolic in a strong sense. We show that for a dense set of maps in the family the geometric Gibbs states do not converge at positive temperature. These are the first examples of non-convergence at positive temperature in statistical mechanics or the thermodynamic formalism, and answers a question of van Enter and Ruszel. We also show that this phenomenon is robust: There is an open set of analytic 2-parameter families of quadratic-like maps that exhibit sensitive dependence of geometric Gibbs states at positive temperature.