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Metric diophantine approximation on ...

Bernik, V. I.

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Metric diophantine approximation on manifolds

Record Type:	Electronic resources : Monograph/item
Title/Author:	Metric diophantine approximation on manifolds/ V.I. Bernik, M.M. Dodson.
Author:	Bernik, V. I.
other author:	Dodson, M. M.
Published:	Cambridge :Cambridge University Press, : 1999.,
Description:	xi, 172 p. :ill., digital ;24 cm.
Notes:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
Subject:	Diophantine approximation. -
Online resource:	https://doi.org/10.1017/CBO9780511565991
ISBN:	9780511565991

Metric diophantine approximation on manifolds
Bernik, V. I.

Metric diophantine approximation on manifolds[electronic resource] /V.I. Bernik, M.M. Dodson. - Cambridge :Cambridge University Press,1999. - xi, 172 p. :ill., digital ;24 cm. - Cambridge tracts in mathematics ;137. - Cambridge tracts in mathematics ;137..

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Diophantine approximation and manifolds --

This 1999 book is concerned with Diophantine approximation on smooth manifolds embedded in Euclidean space, and its aim is to develop a coherent body of theory comparable with that which already exists for classical Diophantine approximation. In particular, this book deals with Khintchine-type theorems and with the Hausdorff dimension of the associated null sets. After setting out the necessary background material, the authors give a full discussion of Hausdorff dimension and its uses in Diophantine approximation. A wide range of techniques from the number theory arsenal are used to obtain the upper and lower bounds required, and this is an indication of the difficulty of some of the questions considered. The authors go on to consider briefly the p-adic case, and they conclude with a chapter on some applications of metric Diophantine approximation. All researchers with an interest in Diophantine approximation will welcome this book.

ISBN: 9780511565991Subjects--Topical Terms:

705002
Diophantine approximation.

LC Class. No.: QA242 / .B5 1999

Dewey Class. No.: 512.73

Metric diophantine approximation on manifolds
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100 1 $a Bernik, V. I. $q (Vasilii Ivanovich) $3 3470693
245 1 0 $a Metric diophantine approximation on manifolds $h [electronic resource] / $c V.I. Bernik, M.M. Dodson.
260 $a Cambridge : $b Cambridge University Press, $c 1999.
300 $a xi, 172 p. : $b ill., digital ; $c 24 cm.
490 1 $a Cambridge tracts in mathematics ; $v 137
500 $a Title from publisher's bibliographic system (viewed on 05 Oct 2015).
505 0 0 $t Diophantine approximation and manifolds -- $t Diophantine approximation in one dimension -- $t Approximation in higher dimensions -- $t Euclidean submanifolds -- $t Metric Diophantine approximation on manifolds -- $t Khintchine's and Groshev's theorems for manifolds -- $t Extremal manifolds -- $t Khintchine and Groshev type manifolds -- $t Baker's conjecture -- $t Higher dimensional manifolds -- $t Hausdorff measure and dimension -- $t Hausdorff measure -- $t Hausdorff dimension -- $t Properties of Hausdorff dimension -- $t Determining the Hausdorff dimension -- $t Hausdorff dimension on manifolds -- $t Upper bounds for Hausdorff dimension -- $t Diophantine approximation on manifolds -- $t Smooth manifolds of dimension at least 2 -- $t Simultaneous Diophantine approximation -- $t Lower bounds for Hausdorff dimension -- $t Regular systems -- $t Ubiquitous systems -- $t Simultaneous Diophantine approximation on manifolds -- $t Diophantine approximation over the p-adic field -- $t Introduction to p-adic numbers -- $t Diophantine approximation in Q[subscript p] -- $t Integral polynomials with small p-adic values -- $t Applications -- $t Diophantine type and very well approximable numbers -- $t A wave equation -- $t The rotation number -- $t Dynamical systems -- $t Linearising diffeomorphisms -- $t Diophantine approximation in hyperbolic space.
520 $a This 1999 book is concerned with Diophantine approximation on smooth manifolds embedded in Euclidean space, and its aim is to develop a coherent body of theory comparable with that which already exists for classical Diophantine approximation. In particular, this book deals with Khintchine-type theorems and with the Hausdorff dimension of the associated null sets. After setting out the necessary background material, the authors give a full discussion of Hausdorff dimension and its uses in Diophantine approximation. A wide range of techniques from the number theory arsenal are used to obtain the upper and lower bounds required, and this is an indication of the difficulty of some of the questions considered. The authors go on to consider briefly the p-adic case, and they conclude with a chapter on some applications of metric Diophantine approximation. All researchers with an interest in Diophantine approximation will welcome this book.
650 0 $a Diophantine approximation. $3 705002
650 0 $a Manifolds (Mathematics) $3 612607
650 0 $a Hausdorff measures. $3 709118
700 1 $a Dodson, M. M. $3 753028
830 0 $a Cambridge tracts in mathematics ; $v 137. $3 3470694
856 4 0 $u https://doi.org/10.1017/CBO9780511565991