Southwest Regional Workshop on New Directions in Dynamical Systems

西南地区动力系统新方向研讨会

• 批准号: 9619881
• 负责人: R. Daniel Mauldin
• 金额: $ 2万
• 依托单位: University of North Texas
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1997
• 资助国家: 美国
• 起止时间: 1997-03-15 至 1999-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9619881&HistoricalAwards=false
• 关键词: Southwest; Regional; Workshop; New; Directions

9619881 This award is for support of a conference/workshop in dynamical systems at the Department of Mathematics of the University of North Texas. Speakers at the workshop will include Professors Katok (Penn State), Keane (CWI, Amsterdam), Przytycki (IM PAN, Warsaw) and Strein (University of Amsterdam). Participants in the workshop will include scholars form the Southwestern US and Northern Mexico. Dynamical systems theory describes processes that develop over time. In particular, dynamical systems arise in physics (Lorenz map), biology and environmental studies (population dynamics) and chemistry (e.g. modeling the Belousov-Zhabotinskii reaction). The development of the system depends on its initial state and parameters coming from the "environment." It is of great importance that we understand the future behavior which may be exhibited by the system for the "majority" of its initial states; this corresponds to the description of so-called attractors to which the first part of the project is devoted. Also in the first part of the proposal we study how properties of some important dynamical systems depend on "environmental" parameters. Sometimes phenomena exhibited by a system are related to one another and information about some of them allows one to make a judgment about the existence of others; in other words phenomena coexist. A good example here is periodicity, i.e. cyclic occurrence of the same states in the system. It turns out that the existence of a cyclic process with a given period for some initial state guarantees that another cyclic process with a different period can be realized for a different initial state and the same environment. In the second part of the project we plan to thoroughly study this relationship between different periods of cyclic processes in the same system.

9619881 该奖项是为了支持北德克萨斯大学数学系动力系统会议/研讨会。 研讨会的演讲者将包括Katok教授（宾夕法尼亚州立大学），Keane教授（CWI，阿姆斯特丹），Przytycki教授（IM PAN，华沙）和Strein教授（阿姆斯特丹大学）。 研讨会的参与者将包括来自美国西南部和墨西哥北方的学者。 动力系统理论描述了随着时间的推移而发展的过程。特别是，动力系统出现在物理学（洛伦兹地图），生物学和环境研究（人口动力学）和化学（例如建模Belousov-Zhabotinskii反应）。系统的发展依赖于系统的初始状态和来自“环境”的参数。“我们理解系统在其初始状态的“大多数”中可能表现出的未来行为是非常重要的;这对应于项目第一部分专门描述的所谓吸引子。此外，在第一部分的建议，我们研究了一些重要的动力系统的属性取决于“环境”参数。有时候，一个系统所表现出来的现象是相互关联的，关于其中一些现象的信息可以让人们对其他现象的存在做出判断;换句话说，现象是共存的。这里的一个很好的例子是周期性，即系统中相同状态的周期性出现。结果表明，对于某个初始状态，存在一个给定周期的循环过程，保证了对于不同的初始状态和相同的环境，可以实现另一个不同周期的循环过程。 在项目的第二部分中，我们计划深入研究同一系统中不同周期循环过程之间的关系。