Renormalization group method in the theory of dynamical systems
Renormalization group method in the theory of dynamical systems
复制标题
动力系统理论中的重整化群方法
DOI：
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发表时间：
1988
期刊：
影响因子：
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通讯作者：
K. Khanin
中科院分区：
文献类型：
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作者：
Y. Sinai;K. Khanin
在过去的十年中，动力系统理论中最重要的事件之一已经成为思想和重整化群方法（RG）到这个传统的数学物理领域的广泛渗透。RG方法是统计物理学中的主要工具之一，在解决涉及新类型分叉的动力系统理论问题时，它已被证明是相当有效的（见下文）。在统计力学中，RG方法的应用是非常感兴趣的临界点附近的有序-混沌过渡。首先，RG-方法被应用于开拓性的论文，致力于一个随机制度的外观作为一个结果的无限序列的倍周期分岔。目前这种随机性机制是研究最多的一种机制，许多论文都在研究它。对所谓的非线性现象的研究是RG方法应用的下一个例子，即研究随机行为域和规则行为域沿动力系统的轨迹沿着交替的情况。
One of the most important events in the theory of dynamical systems for the last decade has become a wide penetration of ideas and renormalization group methods (RG) into this traditional field of mathematical physics. RG-method has been one of the main tools in statistical physics and it has proved to be rather effective while solving problems of the theory of dynamical systems referring to new types of bifurcations (see further). As in statistical mechanics the application of the RG-method is of great interest in the neighborhood of the critical point concerning the order-chaos transition. First the RG-method was applied in the pioneering papers dedicated to the appearance of a stochastical regime as a result of infinite sequences of period doubling bifurcations. At present this stochasticity mechanism is the most studied one and many papers deal with it. The study of the so-called intermittency phenomenon was the next example of application of the RG-method, i.e. the study of such a situation where the domains of the stochastical and regular behavior do alternate along a trajectory of the dynamical system.