Metric diophantine approximation on manifolds

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Metric diophantine approximation on manifolds / V.I. Bernik, M.M. Dodson

資料種別:

図書

出版情報:

Cambridge [Cambridgeshire] : Cambridge University Press, 1999

形態:

xi, 172 p. ; 24 cm

シリーズ名:

Cambridge tracts in mathematics ; v. 137 <BA00134372>

著者名:

ISBN:

9780521432757 [0521432758] (: hbk)

書誌ID:

BA44251351

子書誌情報

フルテキスト

所蔵情報

他の版・巻

書誌詳細

注記:

Includes bibliographical references (p. [161]-170) and index

主題:

Diophantine analysis; Manifolds; Measure theory

言語:

英語

目次情報:

Preface

Notation

Diophantine approximation and manifolds / Chapter 1.：

Introduction / 1.1.：

Diophantine approximation in one dimension / 1.2.：

Approximation in higher dimensions / 1.3.：

Euclidean submanifolds / 1.4.：

Metric Diophantine approximation on manifolds / 1.5.：

Notes / 1.6.：

Khintchine's and Groshev's theorems for manifolds / Chapter 2.：

Extremal manifolds / 2.1.：

Khintchine and Groshev type manifolds / 2.3.：

Baker's conjecture / 2.4.：

Higher dimensional manifolds / 2.5.：

Hausdorff measure and dimension / 2.6.：

Hausdorff measure / 3.1.：

Hausdorff dimension / 3.3.：

Properties of Hausdorff dimension / 3.4.：

Determining the Hausdorff dimension / 3.5.：

Hausdorff dimension on manifolds / 3.6.：

Upper bounds for Hausdorff dimension / 3.7.：

Diophantine approximation on manifolds / 4.1.：

Smooth manifolds of dimension at least 2 / 4.3.：

Simultaneous Diophantine approximation / 4.4.：

Lower bounds for Hausdorff dimension / 4.5.：

Regular systems / 5.1.：

Ubiquitous systems / 5.3.：

Simultaneous Diophantine approximation on manifolds / 5.4.：

Diophantine approximation over the p-adic field / 5.5.：

Introduction to p-adic numbers / 6.1.：

Diophantine approximation in Q[subscript p] / 6.2.：

Integral polynomials with small p-adic values / 6.3.：

Applications / 6.4.：

Diophantine type and very well approximable numbers / 7.1.：

A wave equation / 7.3.：

The rotation number / 7.4.：

Dynamical systems / 7.5.：

Linearising diffeomorphisms / 7.6.：

Diophantine approximation in hyperbolic space / 7.7.：

References / 7.8.：

Index

Preface

Notation

Diophantine approximation and manifolds / Chapter 1.：

Introduction / 1.1.：

Diophantine approximation in one dimension / 1.2.：

Approximation in higher dimensions / 1.3.：

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