Venegeroles Roberto
Centro de Matemática, Computação e Cognição, Universidade Federal do ABC, 09210-170 Santo André, São Paulo, Brazil.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Feb;77(2 Pt 2):027201. doi: 10.1103/PhysRevE.77.027201. Epub 2008 Feb 15.
Recent investigations in nonlinear sciences show that not only hyperbolic but also mixed dynamical systems may exhibit exponential relaxation in the chaotic regime. The relaxation rates, which lead the decay of probability distributions and correlation functions, are related to the classical evolution resolvent (Perron-Frobenius operator) pole logarithm, the so-called Pollicott-Ruelle resonances. In this Brief Report, the leading Pollicott-Ruelle resonances are calculated analytically for a general class of area-preserving maps. Besides the leading resonances related to the diffusive modes of momentum dynamics (slow rate), we also calculate the leading faster rate, related to the angular correlations. The analytical results are compared to the existing results in the literature.
非线性科学领域最近的研究表明，不仅双曲动力系统，而且混合动力系统在混沌状态下都可能呈现指数弛豫。导致概率分布和相关函数衰减的弛豫率，与经典演化预解式（佩龙 - 弗罗贝尼乌斯算子）极点对数相关，即所谓的波利科特 - 鲁埃勒共振。在本简报中，针对一类一般的保面积映射，解析计算了主导的波利科特 - 鲁埃勒共振。除了与动量动力学扩散模式相关的主导共振（慢速率）外，我们还计算了与角关联相关的更快主导速率。将解析结果与文献中的现有结果进行了比较。
