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 动力学这一新兴领域受到了世界各地的广泛关注，其中包括 J.-C. 在法兰西学院开设的一门课程。 Yoccoz，2000。该学科有望在不久的将来为数论、拓扑动力学和遍历理论的研究带来新的发展。 在定于 2005 年 5 月举行的为期三天的研讨会中，在这三个数学领域具有优势的参与者将通过关于迄今为止已出现的工作的讲座和讨论来交流思想，从而有助于为该学科的未来研究产生想法。 即使在作为一个研究领域存在的相对几年里，p 进动力学也因其与复杂动力学的相似性和对比而吸引了许多动力学家和遍历理论家的兴趣，也因其在函数迭代研究中的应用而吸引了数论学家的兴趣。全球领域。 许多基本定理和令人惊讶的病态例子已经被发现，同时几个猜想已经成为该学科中的关键开放问题。遍历理论和动力系统是相对年轻的学科，其发展目的是研究非线性系统的混沌和看似随机的行为。 他们对混沌行为的描述在物理学和工程学中得到了无数的应用。 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其至今仍然充满活力和强大，甚至在密码学和编码理论中找到了应用。 现在，p-adic 动力学为这些充满活力的主题提供了一个机会，以最终有可能提供对所有这些应用的进一步理解的方式进行交互。