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从世界各地受到了相当多的注意，其中包括J.-C。给大学的学院缩减课程。 Yoccoz于2000年。该主题有望在不久的将来进行数字理论，拓扑动力学和阵尾理论的新开发。 在2005年5月的为期三天的讲习班中，在这三个数学领域中具有优势的参与者将通过讲座和讨论迄今为止出现的工作进行交流思想，从而为这一主题提供了未来的研究。 即使在其作为研究领域的存在相对较少的情况下，P-Adic动力学也从许多动态学家和雄性理论家中吸引了兴趣，因为其相似之处是其相似之处，并与复杂的动力学以及对全球领域的迭代界限的应用程序的应用。 已经发现了许多基本定理和不断发展的病理示例，而同时，有几个猜想是该主题中的关键开放式概述的同时。基因理论和动力学系统相对较小，是相对年轻的主题，以研究融合的和看似随机的行为。 他们对混乱行为的描述导致了物理和工程中的tomyriad应用。 另一方面，数字理论是自古以来就已经进行了研究的主题，但其美丽和复杂性使它活在前面的日子里，甚至已经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，以最终有可能进一步理解所有这些plice依的方式进行互动。