Workshop on P-Adic Dynamics

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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.