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Metric diophantine approximation on manifolds

Author: V I Bernik; M M Dodson
Publisher: Cambridge, UK ; New York, NY : Cambridge University Press, 1999.
Series: Cambridge tracts in mathematics, 137.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
"This 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." "All researchers with an interest in Diophantine  Read more...
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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: V I Bernik; M M Dodson
ISBN: 0521432758 9780521432757
OCLC Number: 41212802
Description: xi, 172 pages ; 24 cm.
Contents: Diophantine approximation and manifolds --
Diophantine approximation in one dimension --
Approximation in higher dimensions --
Euclidean submanifolds --
Metric Diophantine approximation on manifolds --
Khintchine's and Groshev's theorems for manifolds --
Extremal manifolds --
Khintchine and Groshev type manifolds --
Baker's conjecture --
Higher dimensional manifolds --
Hausdorff measure and dimension --
Hausdorff measure --
Hausdorff dimension --
Properties of Hausdorff dimension --
Determining the Hausdorff dimension --
Hausdorff dimension on manifolds --
Upper bounds for Hausdorff dimension --
Diophantine approximation on manifolds --
Smooth manifolds of dimension at least 2 --
Simultaneous Diophantine approximation --
Lower bounds for Hausdorff dimension --
Regular systems --
Ubiquitous systems --
Simultaneous Diophantine approximation on manifolds --
Diophantine approximation over the p-adic field --
Introduction to p-adic numbers --
Diophantine approximation in Q[subscript p] --
Integral polynomials with small p-adic values --
Applications --
Diophantine type and very well approximable numbers --
A wave equation --
The rotation number --
Dynamical systems --
Linearising diffeomorphisms --
Diophantine approximation in hyperbolic space.
Series Title: Cambridge tracts in mathematics, 137.
Responsibility: V.I. Bernik, M.M. Dodson.
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Abstract:

This 1999 book is concerned with Diophantine approximation on smooth manifolds embedded in Euclidean space.  Read more...

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'This book is an important addition to the literature from authors who are leading experts in this field.' Glyn Harman, Bulletin of the London Mathematical Society '... carefully written, with an Read more...

 
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