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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Vector & tensor analysis

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Small Divisors in One Dimension (Paperback) Loot Price: R877
Discovery Miles 8 770
Small Divisors in One Dimension (Paperback): J.-C. Yoccoz

Small Divisors in One Dimension (Paperback)

J.-C. Yoccoz; Translated by Duncan Sands

Series: London Mathematical Society Lecture Note Series, 266

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Loot Price R877 Discovery Miles 8 770 | Repayment Terms: R80 pm x 12*

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This book falls into two parts. The first studies those circle diffeomorphisms which commute with a diffeomorphism f whose rotation number r(f) is irrational. When f is not smoothly conjugated to a rotation, its rotation number r(f), according to Herman's theory, cannot be Diophantine. The centralizer, f, thus reflects how good are the rational and Diophantine approximations of r. The second part is dedicated to the study of biholomorphisms of a complex variable in the neighbourhood of a fixed point. In 1942 Siegel demonstrated that such a germ is analytically linearizable if its linear part is a Diophantine rotation; the arithmetic condition imposed on the rotation number was then weakened by Bruno. A geometrical approach to the problem yields an alternative proof of this result and also demonstrates the converse. If the Bruno's arithmetic condition is not satisfied the corresponding quadratic polynomial is not linearizable.

General

Imprint: Cambridge UniversityPress
Country of origin: United Kingdom
Series: London Mathematical Society Lecture Note Series, 266
Release date: June 2020
Authors: J.-C. Yoccoz
Translators: Duncan Sands
Format: Paperback
Pages: 250
ISBN-13: 978-0-521-66257-4
Categories: Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Vector & tensor analysis
LSN: 0-521-66257-5
Barcode: 9780521662574

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