Mathematical Sciences: Transport and Long Time Stability Dynamical Systems

9505017大仲马拟议的研究是在动力系统领域，特别是哈密顿系统的平均化和稳定性。研究人员建议将Anosov平均定理推广到对驱动流有更一般假设的系统；建议将Lasker频率分析应用于辛映射中的输运研究。哈密顿系统出现在天体力学、加速器物理学和自然界的其他领域。由Lasker最先提出的频率分析方法可以应用于各种这样的系统，以检测长时间不稳定性。本研究试图为这一方法提供一个严谨的理论框架。

9505017 Dumas The proposed research is in the area of dynamical systems; in particular, averaging and stability of Hamiltonian systems are to be investigated. The investigator proposes to generalize Anosov's averaging theorem to systems with more general hypotheses on the driving flow; proposes to apply Lasker's frequency analysis to the study of transport in symplectic maps. Hamiltonian systems arise in celestial mechanics, accelerator physics and elsewhere in nature. The frequency analysis method, first developed by Lasker, can be applied to a variety of such systems to detect long time instability. The proposed research seeks to provide a rigorous theoretical framework for this method.