Workshop on P-Adic Dynamics

P-Adic 动力学研讨会

• 批准号: 0500587
• 负责人: Robert Benedetto
• 金额: $ 0.6万
• 依托单位: Amherst College
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-04-15 至 2006-03-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0500587&HistoricalAwards=false
• 关键词: Workshop; Adic; Dynamics

The emerging field of p-adic dynamics has received a sizable amount ofattention from around the world, including a course at the College deFrance given by J.-C. Yoccoz in 2000. The subject promises newdevelopments in the near future for research in number theory,topological dynamics, and ergodic theory. In this three-day workshopscheduled for May, 2005, participants with strengths in these threefields of mathematics will exchange ideas via lectures and discussionsconcerning the work which has appeared up to now, helping to generateideas for future research in this subject. Even in the relatively fewyears of its existence as a research area, p-adic dynamics hasattracted interest from a number of dynamicists and ergodic theoristsfor its parallels and contrasts with complex dynamics, as well as fromnumber theorists for its applications to the study of iteration offunctions over global fields. A number of fundamental theorems andsurprising pathological examples have already been discovered, whileat the same time several conjectures have emerged as key openquestions in the subject.Ergodic theory and dynamical systems are relatively young subjectswhich evolved to study the chaotic and seemingly random behavior ofnonlinear systems. Their descriptions of chaotic behavior have led tomyriad applications in physics and engineering. On the other hand,number theory is a subject which has been studied since ancient times,but whose beauty and intricacy has kept it alive and strong into thepresent day, where it has even found applications in cryptography andcoding theory. Now, p-adic dynamics provides an opportunity forthese vibrant subjects to interact in a way that ultimately hasthe potential to provide further understanding of all theseapplications.

p-adic动力学的新兴领域已经受到了来自世界各地的相当大的关注，包括法国学院的J. C. 2000年的Yoccoz。 这一课题为数论、拓扑动力学和遍历理论的研究在不久的将来提供了新的发展。 在2005年5月举行的为期三天的研讨会上，在这三个数学领域具有优势的与会者将通过讲座和讨论来交流有关迄今为止出现的工作的想法，帮助产生对这一主题未来研究的想法。 即使在它作为一个研究领域存在的相对较短的几年里，p-adic动力学已经吸引了许多动力学家和遍历理论家的兴趣，因为它与复动力学的相似之处和对比，以及数论家的兴趣，因为它应用于研究全局域上的迭代函数。 许多基本定理和令人惊讶的病理学例子已经被发现，同时，一些理论已经成为该学科的关键开放问题。遍历理论和动力系统是相对年轻的学科，它们是为了研究非线性系统的混沌和看似随机的行为而发展起来的。 他们对混沌行为的描述在物理学和工程学中有着广泛的应用。 另一方面，数论是一门自古以来就被研究的学科，但它的美丽和复杂性使它一直保持活力和强大到今天，它甚至在密码学和编码理论中找到了应用。 现在，p-adic动力学提供了一个机会让这些充满活力的学科以一种最终有潜力提供对所有这些应用的进一步理解的方式进行互动。