论文标题
保留Lebesgue措施的无限长期性
Infinite Ergodicity that Preserves the Lebesgue Measure
论文作者
论文摘要
我们证明，对于一定数量的一维动力学系统，它们可以保留Lebesgue度量，并且对该措施（无限的厄尔及性）是善良的。被考虑的系统连接了精确动力学系统的参数区域，并在其中耗散系统的参数区域，并对应于弱混沌发生的参数的临界点（Lyapunov指数收敛到零）。这些结果是R. Adler和B. Weiss对工作的概括。我们表明，通过数值仿真，对这些系统的归一化Lyapunov指数的分布遵守了订单$ 1/2 $的分布。
We proved that for the countably infinite number of one-parameterized one dimensional dynamical systems, they preserve the Lebesgue measure and they are ergodic for the measure (infinite ergodicity). Considered systems connect the parameter region in which dynamical systems are exact and the parameter region in which systems are dissipative, and correspond to the critical points of the parameter in which weak chaos occurs (the Lyapunov exponent converges to zero). These results are the generalization of the work by R. Adler and B. Weiss. We show that the distributions of normalized Lyapunov exponent for these systems obey the Mittag-Leffler distribution of order $1/2$ by numerical simulation.
