Dynamics in One Non-Archimedean Variable

Dynamics in One Non-Archimedean Variable
Author :
Publisher : American Mathematical Soc.
Total Pages : 486
Release :
ISBN-10 : 9781470446888
ISBN-13 : 147044688X
Rating : 4/5 (88X Downloads)

Book Synopsis Dynamics in One Non-Archimedean Variable by : Robert L. Benedetto

Download or read book Dynamics in One Non-Archimedean Variable written by Robert L. Benedetto and published by American Mathematical Soc.. This book was released on 2019-03-05 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Dynamics in One Non-Archimedean Variable Related Books

Dynamics in One Non-Archimedean Variable
Language: en
Pages: 486
Authors: Robert L. Benedetto
Categories: Mathematics
Type: BOOK - Published: 2019-03-05 - Publisher: American Mathematical Soc.

GET EBOOK

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 actin
Topological and Ergodic Theory of Symbolic Dynamics
Language: en
Pages: 481
Authors: Henk Bruin
Categories: Mathematics
Type: BOOK - Published: 2023-01-20 - Publisher: American Mathematical Society

GET EBOOK

Symbolic dynamics is essential in the study of dynamical systems of various types and is connected to many other fields such as stochastic processes, ergodic th
p-adic Numbers
Language: en
Pages: 371
Authors: Fernando Q. GouvĂȘa
Categories: Mathematics
Type: BOOK - Published: 2020-06-19 - Publisher: Springer Nature

GET EBOOK

There are numbers of all kinds: rational, real, complex, p-adic. The p-adic numbers are less well known than the others, but they play a fundamental role in num
Groups and Topological Dynamics
Language: en
Pages: 708
Authors: Volodymyr Nekrashevych
Categories: Mathematics
Type: BOOK - Published: 2022-10-11 - Publisher: American Mathematical Society

GET EBOOK

This book is devoted to group-theoretic aspects of topological dynamics such as studying groups using their actions on topological spaces, using group theory to
A First Course in Fractional Sobolev Spaces
Language: en
Pages: 605
Authors: Giovanni Leoni
Categories: Mathematics
Type: BOOK - Published: 2023-04-12 - Publisher: American Mathematical Society

GET EBOOK

This book provides a gentle introduction to fractional Sobolev spaces which play a central role in the calculus of variations, partial differential equations, a