GIBBS MEASURES IN ERGODIC THEORY
GIBBS MEASURES IN ERGODIC THEORY
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DOI：
10.1070/rm1972v027n04abeh001383
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发表时间：
1972-08
影响因子：
0.9
通讯作者：
Y. Sinai
中科院分区：
文献类型：
--
作者：
Y. Sinai
在本文中，我们引入了吉布斯测度的概念，它推广了统计物理学中的平衡吉布斯分布的概念。这一新概念在Anosov动力系统的研究中具有重要意义。通过这个概念，我们构建了广泛的一类不变的措施，这种动力系统和调查的问题存在的不变的措施一致的光滑结构的流形上，我们还研究了小随机激励下的行为。离散时间和连续时间的情况分别处理。
In this paper we introduce the concept of a Gibbs measure, which generalizes the concept of an equilibrium Gibbs distribution in statistical physics. The new concept is important in the study of Anosov dynamical systems. By means of this concept we construct a wide class of invariant measures for dynamical systems of this kind and investigate the problem of the existence of an invariant measure consistent with a smooth structure on the manifold; we also study the behaviour under small random excitations as . The cases of discrete time and continuous time are treated separately.