Robert L. Benedetto Dynamics in One Non-Archimedean Variable 9781470446888

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Автор: Robert L. Benedetto
Название: Dynamics in One Non-Archimedean Variable
ISBN: 9781470446888
Издательство: Mare Nostrum (Eurospan)
Классификация:

Алгебра

Геометрия

Алгебраическая геометрия

ISBN-10: 147044688X
Обложка/Формат: Hardback
Страницы: 418
Вес: 1.13 кг.
Дата издания: 30.04.2019
Серия: Graduate studies in mathematics
Язык: English
Размер: 187 x 265 x 32
Читательская аудитория: Professional and scholarly
Ключевые слова: Algebra,Algebraic geometry
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Поставляется из: Англии
Описание: 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-Leteliers 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.
Дополнительное описание: Algebra|Algebraic geometry

Dynamics in One Non-Archimedean Variable, Robert L. Benedetto