Chaos in Higher Dimensions

9987468 Gilmore许多物理系统可以表现出混沌行为。 示例包括：振荡化学系统;激光器被驱动超过其稳定阈值;流体在通道中流动;血液在动脉中流动;神经元发送信号;大型耦合电系统;等等。混沌行为简单地说，这类系统产生的信号是确定性的（可预测的），振荡的，而不是周期性的。在我们希望深入理解混沌行为之前，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。 在生物学学科中也面临着类似的问题，并得到了解决（例如，Linneaus）和化学（例如，门捷列夫）的科学家谁能够组织一个结构，为各自的领域。 主要研究者已经开始了物理系统的分类方案，通过为所有低维混沌动力系统创建一个分类方案，可以表现出混沌行为。 他还详细描述了如何从实验数据中提取对这些系统进行分类所必需的信息。Gilmore，Topological analysis of chaotic dynamic systems，Reviews of Modern Physics 70（4），1455-1530（1998））。 根据目前的资助，他将把这种分类方法扩展到高维动力系统。

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.