Dynamics of Homogeneous Spaces and Diophantine Approximation on Manifolds
Author : Anish Ghosh
Publisher :
Page : 49 pages
File Size : 46,20 MB
Release : 2006
Category : Diophantine approximation
ISBN :
Author : Anish Ghosh
Publisher :
Page : 49 pages
File Size : 46,20 MB
Release : 2006
Category : Diophantine approximation
ISBN :
Author : Dmitry Y. Kleinbock
Publisher :
Page : 19 pages
File Size : 34,71 MB
Release : 1997
Category :
ISBN :
Author : V. I. Bernik
Publisher : Cambridge University Press
Page : 198 pages
File Size : 42,80 MB
Release : 1999-10-14
Category : Mathematics
ISBN : 9780521432757
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.
Author : Gisbert Wüstholz
Publisher : Cambridge University Press
Page : 378 pages
File Size : 44,59 MB
Release : 2002-09-26
Category : Mathematics
ISBN : 9780521807999
This is a selection of high quality articles on number theory by leading figures.
Author : Pieter Moree
Publisher : American Mathematical Soc.
Page : 347 pages
File Size : 35,96 MB
Release : 2020-02-12
Category : Education
ISBN : 147045100X
This volume contains the proceedings of the conference Dynamics: Topology and Numbers, held from July 2–6, 2018, at the Max Planck Institute for Mathematics, Bonn, Germany. The papers cover diverse fields of mathematics with a unifying theme of relation to dynamical systems. These include arithmetic geometry, flat geometry, complex dynamics, graph theory, relations to number theory, and topological dynamics. The volume is dedicated to the memory of Sergiy Kolyada and also contains some personal accounts of his life and mathematics.
Author : David Fisher
Publisher : University of Chicago Press
Page : 573 pages
File Size : 40,92 MB
Release : 2022-02-07
Category : Mathematics
ISBN : 022680402X
"Mathematicians David Fisher, Dmitry Kleinbock, and Gregory Soifer highlight in this edited collection the foundations and evolution of research by mathematician Gregory Margulis. Margulis is unusual in the degree to which his solutions to particular problems have opened new vistas of mathematics. Margulis' ideas were central, for example, to developments that led to the recent Fields Medals of Elon Lindenstrauss and Maryam Mirzhakhani. The broad goal of this volume is to introduce these areas, their development, their use in current research, and the connections between them. The foremost experts on the topic have written each of the chapters in this volume with a view to making them accessible by graduate students and by experts in other parts of mathematics"--
Author : Dzmitry Badziahin
Publisher : Cambridge University Press
Page : 341 pages
File Size : 46,99 MB
Release : 2016-11-10
Category : Mathematics
ISBN : 1316817776
Written by leading experts, this book explores several directions of current research at the interface between dynamics and analytic number theory. Topics include Diophantine approximation, exponential sums, Ramsey theory, ergodic theory and homogeneous dynamics. The origins of this material lie in the 'Dynamics and Analytic Number Theory' Easter School held at Durham University in 2014. Key concepts, cutting-edge results, and modern techniques that play an essential role in contemporary research are presented in a manner accessible to young researchers, including PhD students. This book will also be useful for established mathematicians. The areas discussed include ubiquitous systems and Cantor-type sets in Diophantine approximation, flows on nilmanifolds and their connections with exponential sums, multiple recurrence and Ramsey theory, counting and equidistribution problems in homogeneous dynamics, and applications of thin groups in number theory. Both dynamical and 'classical' approaches towards number theoretical problems are also provided.
Author : Robert A. Meyers
Publisher : Springer Science & Business Media
Page : 1885 pages
File Size : 47,50 MB
Release : 2011-10-05
Category : Mathematics
ISBN : 1461418054
Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.
Author : F. Tricerri
Publisher : Cambridge University Press
Page : 145 pages
File Size : 21,68 MB
Release : 1983-06-23
Category : Mathematics
ISBN : 0521274893
The central theme of this book is the theorem of Ambrose and Singer, which gives for a connected, complete and simply connected Riemannian manifold a necessary and sufficient condition for it to be homogeneous. This is a local condition which has to be satisfied at all points, and in this way it is a generalization of E. Cartan's method for symmetric spaces. The main aim of the authors is to use this theorem and representation theory to give a classification of homogeneous Riemannian structures on a manifold. There are eight classes, and some of these are discussed in detail. Using the constructive proof of Ambrose and Singer many examples are discussed with special attention to the natural correspondence between the homogeneous structure and the groups acting transitively and effectively as isometrics on the manifold.
Author :
Publisher : World Scientific
Page : 1001 pages
File Size : 27,52 MB
Release :
Category :
ISBN :