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• catalog abstract ""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 approximation will welcome this book."--Jacket.".
• catalog contributor b11519289.
• catalog contributor b11519290.
• catalog created "1999.".
• catalog date "1999".
• catalog date "1999.".
• catalog dateCopyrighted "1999.".
• catalog description ""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 approximation will welcome this book."--Jacket.".
• catalog description "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.".
• catalog description "Includes bibliographical references and index.".
• catalog extent "xi, 172 p. ;".
• catalog identifier "0521432758".
• catalog isPartOf "Cambridge tracts in mathematics ; 137".
• catalog issued "1999".
• catalog issued "1999.".
• catalog language "eng".
• catalog publisher "Cambridge : Cambridge University Press,".
• catalog subject "512.73 21".
• catalog subject "Diophantine approximation.".
• catalog subject "Hausdorff measures.".
• catalog subject "Manifolds (Mathematics).".
• catalog subject "Metric spaces.".
• catalog subject "QA242 .B5 1999".
• catalog tableOfContents "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.".
• catalog title "Metric diophantine approximation on manifolds / V.I. Bernik, M.M. Dodson.".
• catalog type "text".