J un 2 02 1 SELF CONSISTENT TRANSFER OPERATORS IN A WEAK COUPLING REGIME . INVARIANT MEASURES , CONVERGENCE TO EQUILIBRIUM , LINEAR RESPONSE AND CONTROL OF THE STATISTICAL PROPERTIES
J un 2 02 1 SELF CONSISTENT TRANSFER OPERATORS IN A WEAK COUPLING REGIME . INVARIANT MEASURES , CONVERGENCE TO EQUILIBRIUM , LINEAR RESPONSE AND CONTROL OF THE STATISTICAL PROPERTIES
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Jun 2 02 1 弱耦合机制下的自洽转移运营商。
DOI：
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
S. Galatolo
中科院分区：
文献类型：
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作者：
S. Galatolo
我们描述了自洽转移算子理论的一般方法。这些运营商已被引入作为工具的统计特性的研究，大量的所有到所有的相互作用的动力系统进行平均场耦合。我们考虑一个大类的自洽转移算子和证明一般陈述的存在不变的措施，收敛到平衡，统计稳定性和线性响应的速度在“弱耦合”或弱非线性制度。我们适用于不同性质的例子：耦合扩展的地图，耦合系统的加性噪声，系统由不同的地图耦合的平均场相互作用和其他例子的自洽传输运营商不来自耦合地图。我们还考虑了寻找映射之间的最佳耦合的问题，以改变系统的统计特性，在规定的方式。
We describe a general approach to the theory of self consistent transfer operators. These operators have been introduced as tools for the study of the statistical properties of a large number of all to all interacting dynamical systems subjected to a mean field coupling. We consider a large class of self consistent transfer operators and prove general statements about existence of invariant measures, speed of convergence to equilibrium, statistical stability and linear response in a ”weak coupling” or weak nonlinearity regime. We apply the general statements to examples of different nature: coupled expanding maps, coupled systems with additive noise, systems made of different maps coupled by a mean field interaction and other examples of self consistent transfer operators not coming from coupled maps. We also consider the problem of finding the optimal coupling between maps in order to change the statistical properties of the system in a prescribed way.
具有双稳态热力学极限的随机稳定全局耦合图
影响因子：
2.4
作者：
J.-B. Bardet;G. Keller;R. Zweimüller
通讯作者：
R. Zweimüller