Graduate Studies in Mathematics
Volume: 198;
2019;
463 pp;
Hardcover
MSC: Primary 37;
Print ISBN: 978-1-4704-4688-8
Product Code: GSM/198
List Price: $95.00
AMS Member Price: $76.00
MAA Member Price: $85.50
Electronic ISBN: 978-1-4704-5106-6
Product Code: GSM/198.E
List Price: $95.00
AMS Member Price: $76.00
MAA Member Price: $85.50
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Dynamics in One Non-Archimedean Variable
Share this pageRobert L. Benedetto
The theory of complex dynamics in one variable, initiated by Fatou and
Julia in the early twentieth century, concerns the iteration of a
rational function acting on the Riemann sphere. Building on
foundational investigations of \(p\)-adic dynamics in the late twentieth
century, dynamics in one non-archimedean variable is the analogous
theory over non-archimedean fields rather than over the complex
numbers. It is also an essential component of the number-theoretic
study of arithmetic dynamics.
This textbook presents the fundamentals of non-archimedean
dynamics, including a unified exposition of Rivera-Letelier's
classification theorem, as well as results on wandering domains,
repelling periodic points, and equilibrium measures. The Berkovich
projective line, which is the appropriate setting for the associated
Fatou and Julia sets, is developed from the ground up, as are relevant
results in non-archimedean analysis. The presentation is accessible to
graduate students with only first-year courses in algebra and analysis
under their belts, although some previous exposure to non-archimedean
fields, such as the \(p\)-adic numbers, is recommended. The book should
also be a useful reference for more advanced students and researchers
in arithmetic and non-archimedean dynamics.
Readership
Graduate students and researchers interested in arithmetic and non-archimedean dynamics.
Table of Contents
Table of Contents
Dynamics in One Non-Archimedean Variable