标题： 混沌哈密顿系统再审视：生存概率 显示英文标题

标题： Chaotic Hamiltonian systems revisited: Survival probability

摘要： 我们考虑由保面积标准映射描述的动力系统。 已知对于这个系统，$P(t)$，即在相空间某个给定区域中在时间$t$保持的回归次数的归一化数值（所谓“存活概率”）具有幂律渐进行为，$P(t)\sim t^{-\nu}$。 我们提出了新的半经验论据，使我们能够将混沌边界附近的动力系统映射到树状空间边界上的有效“超度规扩散”，该空间的转移速率具有层次结构。 在我们的方法框架内，我们将指数$\nu$估计为$\nu=\ln 2/\ln (1+r_g)\approx 1.44$，其中$r_g=(\sqrt{5}-1)/2$是临界旋转数。 显示英文摘要

摘要： We consider the dynamical system described by the area--preserving standard mapping. It is known for this system that $P(t)$, the normalized number of recurrences staying in some given domain of the phase space at time $t$ (so-clled "survival probability") has the power--law asymptotics, $P(t)\sim t^{-\nu}$. We present new semi--phenomenological arguments which enable us to map the dynamical system near the chaos border onto the effective "ultrametric diffusion" on the boundary of a tree--like space with hierarchically organized transition rates. In the frameworks of our approach we have estimated the exponent $\nu$ as $\nu=\ln 2/\ln (1+r_g)\approx 1.44$, where $r_g=(\sqrt{5}-1)/2$ is the critical rotation number.