Chaos in Higher Dimensions

9987468吉尔莫许多物理系统都会表现出混沌行为。例如：振荡的化学系统；激光被驱动到超过其稳定阈值；流体在通道中流动；血液在动脉中流动；神经元发送信号；大型耦合电子系统；等等。混沌行为简单地意味着由这类系统产生的信号是确定性的(可预测的)、振荡的、不是周期性的。在我们希望对混沌行为有更深的理解之前，我们必须能够对可能存在的不同类型的混沌行为进行分类。在生物学(如Linneaus)和化学(如Mendeleef)学科中，能够为各自领域组织结构的科学家面临并解决了类似的问题。Printon Investigator已经开始了对可能表现出混沌行为的物理系统的分类方案，通过为所有低维混沌动力系统创建分类方案。他还详细描述了如何从实验数据中提取对这类系统进行分类所需的信息(R.Gilmore，《混沌动力系统的拓扑分析》，《现代物理评论》70(4)，1455-1530(1998))。他将在目前的拨款下将这种分类方案扩展到更高维的动力系统。

9987468Gilmore Many physical systems can exhibit chaotic behavior. Examples include: oscillating chemical systems; lasers driven beyond their threshold of stability; fluids flowing in channels; blood flowing inarteries; neurons sending signals; large coupled electrical systems; etc. Chaotic behavior means briefly that the signals generated by such systems are deterministic (predictable), oscillating, andnot periodic. Before we can hope to reach a deep understandingof chaotic behavior, we must be able to classify the different types of chaotic behavior that can exist. Similar problems were faced,andresolved, in the disciplines of Biology (e.g., Linneaus) and Chemistry (e.g., Mendeleef) by scientists who were able to organize a structure for their respective fields. The Principle Investigator has begun the classification scheme for physical systems which can exhibit chaotic behavior by creating a classification scheme for all low dimensional chaotic dynamical systems. He also described in detail how the information necessary to classify such systems can be extractedfrom experimental data (R. Gilmore, Topological analysis of chaotic dynamical systems, Reviews of Modern Physics 70(4), 1455-1530 (1998)). He will extend this classification scheme to higher dimensional dynamical systems under the current grant.