相空间体积守恒动力系统大时间平均运动扰动下的稳定性
Stability under Perturbations of the Large Time Average Motion of Dynamical Systems with Conserved Phase Space Volume
摘要：
利用统计物理形式与遍历理论的相似性，研究了一类广义相空间体积守恒动力系统的摄动稳定性。证明了一个一般的连续性定理。从这个定理的双重平均-时间和合奏-的一个观察的弱扰动遍历动力系统的结果是只有轻微的变化，即使在无限的时间限制。这种统计模拟的结构稳定性的后果是：玻尔兹曼遍历假设的实际适用范围的扩展，在统计物理学中的微扰方法的理由，在分子动力学计算的数值近似的理由和从有界到无界运动的过渡的平滑度观察到在托卡马克的异常输运的数值模拟。
英文摘要：
The stability against perturbations of a dynamical system conserving a generalized phase-space volume is studied by exploiting the similarity between statistical physics formalism and that of ergodic theory. A general continuity theorem is proved. Resulting from this theorem the double average - time and ensemble - of an observable of a weakly perturbed ergodic dynamical system is only slightly changed, even in the infinite time limit. Consequences of this statistical analogue of the structural stability are: extension of the range of practical applicability of the Boltzmann Ergodic Hypothesis, justification of the perturbation method in statistical physics, justification of the numerical approximations in molecular dynamic calculations and smoothness of the transition from bounded to unbounded motion as observed in numerical simulation of anomalous transport in tokamaks.
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